U.S. patent number 7,443,601 [Application Number 11/453,120] was granted by the patent office on 2008-10-28 for zoom optical system.
This patent grant is currently assigned to Canon Kabushiki Kaisha. Invention is credited to Koshi Hatakeyama, Hirofumi Yoshida.
United States Patent |
7,443,601 |
Yoshida , et al. |
October 28, 2008 |
Zoom optical system
Abstract
At least one exemplary embodiment is directed to a zoom optical
system which includes a plurality of variable power optical units
of which optical power varies accompanied by variable power, a
fixed optical unit of which optical power does not vary accompanied
by variable power, and a moving optical unit which moves
accompanied by variable power.
Inventors: |
Yoshida; Hirofumi (Yokohama,
JP), Hatakeyama; Koshi (Kita-ku, JP) |
Assignee: |
Canon Kabushiki Kaisha (Tokyo,
JP)
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Family
ID: |
37567014 |
Appl.
No.: |
11/453,120 |
Filed: |
June 13, 2006 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20060291069 A1 |
Dec 28, 2006 |
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Foreign Application Priority Data
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Jun 27, 2005 [JP] |
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2005-186981 |
Jun 27, 2005 [JP] |
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2005-186984 |
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Current U.S.
Class: |
359/683;
359/720 |
Current CPC
Class: |
G02B
15/04 (20130101) |
Current International
Class: |
G02B
15/14 (20060101) |
Field of
Search: |
;359/676,683,708,720 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
Keisuke Araki, "Paraxial Analysis for Off-Axial Optical Systems",
Japanese Journal of Optics, vol. 29, No. 3, 2000. cited by
other.
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Primary Examiner: Collins; Darryl J
Attorney, Agent or Firm: Canon U.S.A. Inc., IP Division
Claims
What is claimed is:
1. A zoom optical system comprising: a plurality of variable power
optical units of which optical power changes as magnification
varies, wherein the plurality of variable power optical units each
has plural optical elements moving in a direction different from an
optical axis as magnification varies; a fixed optical unit of which
optical power does not change as magnification varies; and a moving
optical unit which moves as magnification varies, wherein when the
maximum value of the absolute value of the optical power in an
optical group of the plurality of variable power optical units is
|.PHI.d| max within the entire range of variable power positions,
and the maximum value of the absolute value of the optical power of
the moving optical unit is |.PHI.s| max within the entire range of
variable power positions, the following condition |.PHI.s| max
<|.PHI.d| max is satisfied.
2. The zoom optical system according to claim 1, wherein the
plurality of variable power optical units each include a rotational
asymmetrical surface and have an optical element for moving in the
direction different from the optical axis.
3. The zoom optical system according to claim 1, wherein the moving
optical unit moves in the direction different from the optical axis
as magnification varies.
4. The zoom optical system according to claim 1, wherein the moving
optical unit moves along the optical axis as magnification
varies.
5. The zoom optical system according to claim 4, wherein when the
amount of movement within the entire zoom range of the moving
optical unit is d, and the entire length of the entire system is T,
the following condition d/T<0.6 is satisfied.
6. The zoom optical system according to claim 1, wherein the moving
optical unit is made up of one optical element.
7. The zoom optical system according to claim 1, wherein the sign
of the optical power of the moving optical unit is unchangeable
over the entire variable power range.
8. The zoom optical system according to claim 1, wherein the moving
optical unit has an optical element for moving in the direction
different from the optical axis; and wherein when the maximum value
of the absolute value of the amount of shift of an optical element
of the plurality of variable optical units within the entire range
of variable power positions is |Dd| max, and the maximum value of
the absolute value of the amount of shift of the optical element of
the moving optical units within the entire range of variable power
positions is |Ds| max, the following condition |Ds| max <|Dd|
max is satisfied.
9. The zoom optical system according to claim 1, wherein the moving
optical unit includes an optical element having positive refracting
power.
10. The zoom optical system according to claim 1, wherein the
plurality of variable power optical units have a first variable
power optical unit and a second variable power optical unit; and
wherein when a greater absolute value of the optical power at the
wide-angle end of the first and second variable power optical units
is |.PHI.gw max, and a smaller absolute value of the optical power
at the telephoto end of the first and second optical units is
|.PHI.gt| min, the following condition |.PHI.gw| max <|.PHI.gt|
min is satisfied.
11. The zoom optical system according to claim 1, wherein the
plurality of variable power optical units have a first variable
power optical unit and a second variable power optical unit; and
wherein when the maximum value of the absolute value of the optical
power in the first and second variable power optical units in the
entire zoom range is |.PHI.| max and .PHI.1 is the first variable
power optical unit optical power and .PHI.2 is the second variable
power optical unit optical power then when the value of sum of the
optical powers in an arbitrary zoom position of the first and
second variable power optical units is .PHI.AB=.PHI.1+.PHI.2, the
following condition -|.PHI.| max .ltoreq..PHI.AB .ltoreq.|.PHI.|
max is satisfied.
12. An imaging apparatus comprising: the zoom optical system
according to claim 1; and a photoelectric conversion element for
photo-accepting an image to be formed by the zoom optical
system.
13. A zoom optical system comprising: a plurality of variable power
optical units of which optical power changes as magnification
varies, wherein the plurality of variable power optical units each
has plural optical elements moving in a direction different from an
optical axis as magnification varies; a fixed optical unit of which
optical power does not change as magnification varies; and a moving
optical unit which moves as magnification varies, wherein the
moving optical unit has an optical element for moving in the
direction different from the optical axis; and wherein when the
maximum value of the absolute value of the amount of shift of an
optical element of the plurality of variable optical units within
the entire range of variable power positions is |Dd| max, and the
maximum value of the absolute value of the amount of shift of the
optical element of the moving optical units within the entire range
of variable power positions is |Ds| max, the following condition
|Ds| max <|Dd| max is satisfied.
14. An imaging apparatus comprising: the zoom optical system
according to claim 13; and a photoelectric conversion element for
photo-accepting an image to be formed by the zoom optical
system.
15. A zoom optical system comprising: a plurality of variable power
optical units of which optical power changes as magnification
varies, wherein the plurality of variable power optical units each
has plural optical elements moving in a direction different from an
optical axis as magnification varies; a fixed optical unit of which
optical power does not change as magnification varies; and a moving
optical unit which moves as magnification varies, wherein when the
amount of movement within the entire zoom range of the moving
optical unit is d, and the entire length of the entire system is T,
the following condition d/T<0.6 is satisfied.
16. An imaging apparatus comprising: the zoom optical system
according to claim 15; and a photoelectric conversion element for
photo-accepting an image to be formed by the zoom optical
system.
17. A zoom optical system comprising: a plurality of variable power
optical units of which optical power changes as magnification
varies, wherein the plurality of variable power optical units each
has plural optical elements moving in a direction different from an
optical axis as magnification varies; a fixed optical unit of which
optical power does not change as magnification varies; and a moving
optical unit which moves as magnification varies, wherein the
plurality of variable power optical units have a first variable
power optical unit and a second variable power optical unit; and
wherein when the maximum value of the absolute value of the optical
power in the first and second variable power optical units in the
entire zoom range is |.PHI.| max and .PHI.1 is the first variable
power optical unit optical power and .PHI.2 is the second variable
power optical unit optical power then when the value of sum of the
optical powers in an arbitrary zoom position of the first and
second variable power optical units is .PHI.AB=.PHI.1+.PHI.2, the
following condition -|.PHI.| max .ltoreq..PHI.AB .ltoreq.|.PHI.|
max is satisfied.
18. An imaging apparatus comprising: the zoom optical system
according to claim 17; and a photoelectric conversion element for
photo-accepting an image to be formed by the zoom optical
system.
19. A zoom optical system comprising: a plurality of variable power
optical units of which optical power changes as magnification
varies, wherein the plurality of variable power optical units each
has plural optical elements moving in a direction different from an
optical axis as magnification varies; a fixed optical unit of which
optical power does not change as magnification varies; and a moving
optical unit which moves in the direction different from the
optical axis as magnification varies.
20. An imaging apparatus comprising: the zoom optical system
according to claim 19; and a photoelectric conversion element for
photo-accepting an image to be formed by the zoom optical system.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a zoom optical system and an
imaging apparatus using the zoom optical system.
2. Description of the Related Art
In recent years, there has been an increased demand for small high
resolution zoom optical systems, such as digital cameras, and
cellular phones with cameras.
With a small high-resolution zoom optical system, zooming is
commonly performed by moving a plurality of lens groups (lens
units) in the optical-axis direction as to a photo-accepting
surface (CCD). At this time, a zoom method for moving lens groups
(lens units) in the object direction causes the entire optical
length (length from a first lens surface to the image plane) to be
lengthened, and this contributes to restricting reductions in size
of the entire lens system.
In order to reduce the above factor, heretofore, an optical system
employing optical elements called Alvarez lenses has been discussed
for changing the power of the entire system by moving the optical
elements in a direction different from the optical-axis direction
(see U.S. Pat. Nos. 3,305,294, 3,583,790, and Optics Vol. 29, No. 3
(2000)).
Subsequently, various types of zoom optical systems for performing
zooming using these Alvarez lenses have been discussed (see
Japanese Patent Laid-Open No. 1990-119103).
With the optical system discussed in U.S. Pat. No. 3,305,294, power
is changed by providing two lenses, which can have a surface
represented with a tertiary function, and shifting these lenses in
the direction different from the optical-axis direction. This
optical system does not send out the lens groups (lens units) in
the optical-axis direction, so employing this for a zoom optical
system can reduce the entire lens length.
Also, the optical system discussed in U.S. Pat. No. 3,583,790
reduces an aberration by providing lenses, which can have a curved
surface represented with an order term higher than a tertiary term,
particularly a quintic term.
Further, in Japanese Patent Laid-Open No. 1990-119103 there is
discussed an example in which two lens are employed for a zoom
optical system. Subsequently, a theory for changing power while
maintaining an image point in a steady manner has been discussed by
disposing at least the two above lenses.
On the other hand, Optics Vol. 29, No. 3 (2000) describes an
optical system including a rotational asymmetric optical element.
This optical system has no common axis (optical axis), which is
different from a normal coaxial lens system. Such a non-coaxial
optical system is called as an Off-Axial optical system, which can
be defined as an optical system including a curved surface
(Off-Axial curved surface) where when assuming that the route in
which the ray passing through the image center and the pupil center
traces is taken as a reference axis, a surface normal at an
intersection with the reference axis of constituent surfaces is not
present on the reference axis. In this case, the reference axis has
a folded and bent shape. Accordingly, this needs to employ a
paraxial theory based on the Off-Axial theory other than the
paraxial theory of a coaxial system such as usually employed for
calculation of the paraxial amount. The optical principle of the
method thereof has been introduced in the optics Vol. 29, No. 3
(2000), which is performed by calculating 4.times.4 determinants
based on a surface curvature, for example.
With U.S. Pat. Nos. 3,305,294, 3,305,294, and 3,583,790,
descriptions have been made regarding a method for changing power
with a pair of rotational asymmetric lenses and correction of an
aberration, but they cannot maintain an image plane in a steady
manner when changing power.
Also, with Japanese Patent Laid-Open No. 1990-119103, the principle
for changing power while maintaining an image point in a steady
manner has been described, but has not reached the design level of
a zoom optical system for obtaining an actual appropriate image by
performing correction of an aberration.
In order to configure a zoom optical system with Alvarez lenses, it
can be necessary in some circumstances to configure the system so
as to have a steady image plane even at the time of zooming, and
reduce the aberration fluctuation due to zooming.
SUMMARY OF THE INVENTION
At least one exemplary embodiment is directed to a zoom optical
system and an imaging apparatus using the zoom optical system for
example a projector, exposure apparatus, and reader.
At least one exemplary embodiment is directed to a zoom optical
system which realizes a steady image plane even at the time of
zooming, less aberration fluctuation due to zooming, high optical
capabilities straddling the entire zoom range, and reduction in the
entire optical length by appropriately employing an optical group,
which can have a plurality of optical elements which include a
rotationally asymmetrical surface and move in the direction
different from the optical axis, and one or more optical
groups.
According to at least one exemplary embodiment, a zoom optical
system includes a plurality of variable power optical units of
which optical power changes as magnification varies, where the
plurality of variable power optical units each has plural optical
elements moving in a direction different from an optical axis as
magnification varies, a fixed optical unit of which optical power
does not change as magnification varies, a moving optical unit
which moves as magnification varies.
According to at least one exemplary embodiment, an imaging
apparatus includes the zoom optical system, and a photoelectric
conversion element for photo-accepting an image to be formed by the
zoom optical system.
Further features and aspects of the present invention will become
apparent from the following description of exemplary embodiments
with reference to the attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a lens cross-sectional view according to an example 1 of
at least one exemplary embodiment.
FIG. 2 is a diagram describing the Off-Axial optical system of a
comparative example 2.
FIG. 3 is a plot of the power allocation of the lens designed based
on the comparative example 1.
FIG. 4 is a cross-sectional view of the lens designed based on the
comparative example 1.
FIG. 5 is a lens cross-sectional view of the comparative example
2.
FIG. 6 is a lens cross-sectional view of the telephoto end, middle,
and wide-angle end according to the comparative example 2.
FIG. 7A is an aberration chart according to the comparative example
2.
FIG. 7B is an aberration chart according to the comparative example
2.
FIG. 7C is an aberration chart according to the comparative example
2.
FIG. 8 is a diagram showing the numbers of the rays on an image
plane according to at least one exemplary embodiment.
FIG. 9 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the
comparative example 2.
FIG. 10 is a lens cross-sectional view according to the example 1
of at least one exemplary embodiment.
FIG. 11A is an aberration chart of the example 1 of at least one
exemplary embodiment.
FIG. 11B is an aberration chart of the example 1 of at least one
exemplary embodiment.
FIG. 11C is an aberration chart of the example 1 of at least one
exemplary embodiment.
FIG. 12 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
1 of at least one exemplary embodiment.
FIG. 13 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 1 of at least
one exemplary embodiment.
FIG. 14 is a chart illustrating change in the principal-point
positions of the G1 and G3 according to the example 1 of at least
one exemplary embodiment.
FIG. 15 is a lens cross-sectional view according to an example 2 of
at least one exemplary embodiment.
FIG. 16 is a lens cross-sectional view of the telephoto end,
middle, and wide-angle end according to the example 2 of at least
one exemplary embodiment.
FIG. 17A is an aberration chart of the example 2 of at least one
exemplary embodiment.
FIG. 17B is an aberration chart of the example 2 of at least one
exemplary embodiment.
FIG. 17C is an aberration chart of the example 2 of at least one
exemplary embodiment.
FIG. 18 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
2 of at least one exemplary embodiment.
FIG. 19 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 2 of at least
one exemplary embodiment.
FIG. 20 is a chart illustrating change in the principal-point
positions of the G1 and G3 according to the example 2 of at least
one exemplary embodiment.
FIG. 21 is a lens cross-sectional view according to an example 3 of
at least one exemplary embodiment.
FIG. 22 is a lens cross-sectional view of the telephoto end,
middle, and wide-angle end according to the example 3 of at least
one exemplary embodiment.
FIG. 23A is an aberration chart of the example 3 of at least one
exemplary embodiment.
FIG. 23B is an aberration chart of the example 3 of at least one
exemplary embodiment.
FIG. 23C is an aberration chart of the example 3 of at least one
exemplary embodiment.
FIG. 24 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
3 of at least one exemplary embodiment.
FIG. 25 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 3 of at least
one exemplary embodiment.
FIG. 26 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 3 of at least
one exemplary embodiment.
FIG. 27 is a lens cross-sectional view according to an example 4 of
at least one exemplary embodiment.
FIG. 28 is a lens cross-sectional view of the telephoto end,
middle, and wide-angle end according to the example 4 of at least
one exemplary embodiment.
FIG. 29A is an aberration chart of the example 4 of at least one
exemplary embodiment.
FIG. 29B is an aberration chart of the example 4 of at least one
exemplary embodiment.
FIG. 29C is an aberration chart of the example 4 of at least one
exemplary embodiment.
FIG. 30 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
4 of at least one exemplary embodiment.
FIG. 31 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 4 of at least
one exemplary embodiment.
FIG. 32 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 4 of at least
one exemplary embodiment.
FIG. 33 is a lens cross-sectional view according to an example 5 of
at least one exemplary embodiment.
FIG. 34 is a lens cross-sectional view of the telephoto end,
middle, and wide-angle end according to the example 5 of at least
one exemplary embodiment.
FIG. 35A is an aberration chart of the example 5 of at least one
exemplary embodiment.
FIG. 35B is an aberration chart of the example 5 of at least one
exemplary embodiment.
FIG. 35C is an aberration chart of the example 5 of at least one
exemplary embodiment.
FIG. 36 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
5 of at least one exemplary embodiment.
FIG. 37 is an explanatory diagram of an imaging apparatus according
to at least one exemplary embodiment.
FIG. 38 is a lens cross-sectional view according to an example 6 of
at least one exemplary embodiment.
FIG. 39 is a lens cross-sectional view according to the example 6
of at least one exemplary embodiment.
FIG. 40A is an aberration chart of the example 6 of at least one
exemplary embodiment.
FIG. 40B is an aberration chart of the example 6 of at least one
exemplary embodiment.
FIG. 40C is an aberration chart of the example 6 of at least one
exemplary embodiment.
FIG. 41 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
6 of at least one exemplary embodiment.
FIG. 42 is a chart illustrating change in power of an optical group
G1 and an optical group G3 according to the example 6 of at least
one exemplary embodiment.
FIG. 43 is a chart illustrating change in the principal-point
positions of the G1 and G3 according to the example 6 of at least
one exemplary embodiment.
FIG. 44 is a lens cross-sectional view according to the example 6
of at least one exemplary embodiment.
FIG. 45 is a lens cross-sectional view according to an example 7 of
at least one exemplary embodiment.
FIG. 46A is an aberration chart of the example 7 of at least one
exemplary embodiment.
FIG. 46B is an aberration chart of the example 7 of at least one
exemplary embodiment.
FIG. 46C is an aberration chart of the example 7 of at least one
exemplary embodiment.
FIG. 47 is a diagram showing the distortion reactor lattices at the
telephoto end, middle, and wide-angle end according to the example
7 of at least one exemplary embodiment.
FIG. 48 is a chart illustrating change in power of an optical group
G1 and an optical group G2 according to the example 7 of at least
one exemplary embodiment.
DESCRIPTION OF THE EMBODIMENTS
The following description of at least one exemplary embodiment is
merely illustrative in nature and is in no way intended to limit
the invention, its application, or uses.
Processes, techniques, apparatus, and materials as known by one of
ordinary skill in the relevant art may not be discussed in detail
but are intended to be part of the enabling description where
appropriate, for example the fabrication of the lens elements and
their materials.
In all of the examples illustrated and discussed, herein any
specific values, for example the zoom ratio and F number, should be
interpreted to be illustrative only and non limiting. Thus, other
examples of the exemplary embodiments could have different
values.
Notice that similar reference numerals and letters refer to similar
items in the following figures, and thus once an item is defined in
one figure, it may not be discussed for following figures.
Note that herein when referring to correcting or corrections of an
error (e.g., an aberration), a reduction of the error and/or a
correction of the error is intended.
First, prior to describing examples of at least one exemplary
embodiment, description will be made regarding the rotationally
asymmetrical surface of the Off-Axial optical system making up the
zoom optical system of at least one exemplary embodiment, and how
to represent configuration specifications thereof.
With the Off-Axial optical system, as shown in FIG. 2 illustrated
as a later-described comparative example 2 of at least one
exemplary embodiment, a surface SO on the light incident side is
taken as a reference plane, and an absolute coordinates system is
set with the center PO of the reference plane SO as the origin. Let
us say that the route traced by a ray passing through the origin PO
and the pupil center is taken as a reference axis. Also, let us say
that the straight line connecting an image center IPO and the
origin of the absolute coordinates system serving as the center PO
of the reference plane SO is taken as the Z axis, and the
orientation headed to the image center from a first surface is
positive. We will refer to this Z axis as the optical axis.
Further, let us say that the Y axis is taken as the straight line
passing through the origin PO, and originating 90 degrees in the
counterclockwise direction as to the Z axis in accordance with the
definition of the right-hand coordinates system, and the X axis is
taken as the straight line passing through the origin, which is
perpendicular to each axis of the Z and Y axes.
The paraxial values shown below are the results of performing
Off-Axial paraxial tracing. Let us say that the Off-Axial paraxial
tracing is performed, and the calculated results are taken as
paraxial values, unless otherwise stated.
An optical system according to at least one exemplary embodiment
has a rotational asymmetric shaped aspheric surface, and the shape
is represented with the following equation.
z=C02y.sup.2+C20x.sup.2+C03y.sup.3+C21x.sup.2y+C04y.sup.4+C22x.sup.2y.sup-
.2+C40x.sup.4+C05y.sup.5+C23x.sup.2y.sup.3+C41x.sup.4y+C06y.sup.6+C24x.sup-
.2y.sup.4+C42x.sup.4y.sup.2+C60x.sup.6 [Equation 1]
Equation 1 has even order terms alone regarding x, so the curved
surface stipulated with Equation 1 has a surface-symmetric shape
which takes the y-z surface (see FIG. 2) as a symmetric
surface.
Also, in the event of satisfying the following condition, the shape
represents a shape symmetric as to the x-z surface (see FIG. 2).
C03=C21=C05=C23=C41=t=0 [Equation 2]
Further, in the event of satisfying the following conditions, the
shape represents a rotational symmetric shape. C02=C20 [Equation 3]
C04=C40=C22/2 [Equation 4] C06=C60=C24/3=C42/3 [Equation 5]
In the event of not satisfying the above conditions, the shape is a
rotational asymmetric shape.
The rotational symmetric surface and rotationally asymmetrical
surface shapes shown in the following examples and comparative
examples are based on Equation 1 through Equation 5.
EXAMPLE 1
FIG. 1 is a lens cross-sectional view according to an example 1 of
at least one exemplary embodiment. In FIG. 1, T, M, and W are lens
cross-sectional views at the telephoto end (the zoom position where
the power of the entire system is the minimum), at a middle zoom
position, and at the wide-angle end (the zoom position where the
power of the entire system is the maximum) respectively.
FIG. 10 is a lens cross-sectional view for selecting the middle
zoom position of example 1 in FIG. 1 (M in FIG. 1) as an example
and describing respective factors.
A zoom optical system according to example 1 is a photography lens
system employed for an imaging apparatus, with the left hand side
the object side, and the right hand side the image side in the lens
cross-sectional view.
Note that the zoom optical system according to example 1 can be
employed as a projector, and in this case, on the left hand side is
a screen, and on the right hand side is a projection surface.
In FIG. 1 and FIG. 10, G1 and G3 are optical groups in which
optical power is variable (optical power and focal distance vary at
the time of zooming of the zoom optical system in the present
example). G2 is an optical group in which optical power is
substantially unchangeable (essentially unchangeable).
G4 is an optical group having symmetry as to at least one surface
(one surface taken as a symmetric center), and including one or
more optical elements Ls capable of decentering. With the present
example, the term "optical group" is employed, but this can be
referred to as "optical unit", "lens unit", or "lens group." In
other words, the optical elements Ls can have a rotational
asymmetric shape symmetric as to multiple surfaces (e.g., toric
surfaces or other related or equivalent surfaces as known by one of
ordinary skill in the relevant art), but in at least one exemplary
embodiment, which are optical elements having a rotational
asymmetric shaped surface symmetric as to only one surface (only
one surface serving as a symmetric center exists). This can be also
applied to the optical elements included in the G1 and G3.
Zooming is performed while maintaining the image plane IP in a
steady manner by changing the power of the two optical groups G1
and G3 each of which optical power is variable.
The two optical groups G1 and G3 each of which optical power is
variable each include a rotationally asymmetrical surface, move in
the direction substantially different from the optical axis, and
include two optical elements E1 and E2 which change the power
within the optical group G1, and two optical elements E5 and E6
which change the power within the optical group G3,
respectively.
Note that the term "optical power" refers to the power of a surface
positioned on the optical axis, and when the surface on the optical
axis varies by the optical element having a rotationally
asymmetrical surface being decentered, optical power is also
changed in response to that change.
In example 1 of at least one exemplary embodiment, seven optical
elements (lenses) are employed in total. In order from the object
side, the optical elements E1, E2, E5, and E6 have a rotational
asymmetric shape, these optical elements are decentered in the
Y-axis direction, and the amount of decentering continuously
varies. Also, the absolute value of the amount thereof is set so as
to be equal with mutually positive/negative reverse. The optical
elements E3 and E4 have a rotational symmetric spherical surface.
In the event that an asymmetric aberration remains on the optical
axis, the optical elements E3 and E4 can have a rotational
asymmetric shape to reduce this. The optical element E7 has a
rotational asymmetric shape symmetric as to at least one surface.
This reduces the on-axis coma aberration which may not have been
reduced in the optical elements E1 through E6 by shifting or
tilting this aberration. Also, the first group G1 comprises the
optical elements E1 and E2. Similarly, the second group G2
comprises the optical elements E3 and E4, and the third group G3
comprises the optical elements E5 and E6. The fourth group G4
comprises the optical element E7. As for surface numbers, the
reference plane serving as the origin of the absolute coordinates
system is determined as a surface S0, the first surface of the
optical element E1 is determined as S1, and in order, the
corresponding surfaces are surfaces S2, S3, S4, and so on, and
following the surface S6 (backward of the optical element E3) a
diaphragm S7 (SP) is disposed. The first surface of the optical
element E4 is determined as S8, and the subsequent numbers are
assigned in order, and the image plane IP is S16. Hereinafter,
decentering continues in the Y-axis direction, and let us say that
the rotational asymmetric groups (G1 and G3), which contribute to
change in power, the rotational symmetric group (G2), and the
fourth group G4 made up of the optical element (E7) configured to
suppress the above residual aberration by decentering are referred
to as decentering movable blocks G1 and G3, auxiliary block G2, and
auxiliary movable block G4, respectively. Disposing the decentering
movable blocks G1 and G3 alone makes the power thereof too strong,
and can make it difficult to perform correction of an aberration,
and accordingly, the auxiliary block G2 is disposed.
The lens data of the example 1 is shown in Table 7. The amount of
shift from the Z axis of the respective optical elements is shown
in Table 8. The values of the respective coefficients of the
polynomial surfaces represented with Equation 1 are shown in Tables
9-1 and 9-2. FIG. 1 is a lens cross-sectional view at the telephoto
end (T), middle zoom position (M), and wide-angle end (W) shown in
Table 8. The optical elements E1 and E2 are decentered in the
Y-axis direction, and the absolute value of the amount thereof is
so as to be equal with mutually positive/negative reverse, as shown
in Table 8. Thus, the power of the first group G1 is changed from
positive to negative between the telephoto end and the wide-angle
end. The ray emitted from the first group G1 passes through the
optical element E3, diaphragm SP, and optical element E4, and
illuminates the optical elements E5 and E6. The optical elements E5
and E6 are decentered in the Y-axis direction, and the absolute
value of the amount thereof is so as to be equal with mutually
positive/negative reverse, as shown in Table 8. Thus, the power of
the third group G3 is changed from negative to positive between the
telephoto end and the wide-angle end. The ray passed through these
decentering movable blocks G1 and G3 illuminates the next auxiliary
movable block G4. The auxiliary movable block G4 compensates the
power necessary for the decentering movable blocks G1 and G3. The
ray passed through these optical elements forms an image without
changing the image plane IP.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 11A through FIG.
11C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 11A through FIG. 11C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X axis, so only the positive case should be
taken into consideration regarding the X direction. When viewing
the ray at an angle of view of 0.degree., it can be understood that
a coma aberration can be reduced from the telephoto end to the
wide-angle end. Also, FIG. 12 illustrates the distortion reactor
lattices at a telephoto end T, middle zoom position M, and
wide-angle end W. The lengthwise and crosswise size of the lattices
is about 1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm).
When viewing this figure, it can be understood that distortion can
be suppressed, but when viewing the ray at an angle of view of
0.degree., it can be understood that some amount of a coma
aberration can remain.
FIG. 13 is a chart plotting change in power .PHI.1 and .PHI.3 of
the first group G1 and the third group G3 caused by zooming, and
the sum thereof .PHI.13(.PHI.1+.PHI.3) as to the power of the
entire system.
At this time, when assuming that the maximum value of the absolute
value of the power in the first group G1 and the third group G3 is
|.PHI.|max, and the power of the sum of the first group G1 and the
third group G3 is .PHI.13, the following condition
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max can be satisfied.
Satisfying the conditional expression (5) reduces the Petzval sum
and the image plane distortion.
FIG. 14 illustrates change in the principal-point positions before
and after the first group G1 and the third group G3 (H1 is the
forward principal-point position of the first group G1, H1' is the
backward principal-point position of the first group G1, H2 is the
forward principal-point position of the third group G3, and H2' is
the backward principal-point position of the third group G3). The
first group G1 is made up of meniscus-shaped optical elements, so
the principal-point position thereof greatly moves. Also, when
comparing the change thereof with FIG. 13, it can be understood
that the power of the first group G1 moves in the object direction
in the positive range as the power of the entire system increases,
and expands the interval of the H1 and H2. Also, it can be
understood that the power of the first group G1 moves in the object
direction even in the negative range as the power of the entire
system increases, and expands the interval of the H1 and H2. Also,
when assuming that the forward principal-point position and the
backward principal-point position of the first group G1 are H1 and
H1' respectively, the forward principal-point position and the
backward principal-point position of the third group G3 are H2 and
H2' respectively, the distance between the object point and the H1
is eo, the distance between the H1' and H2 is e, the distance
between the H2' and the image point is ei, and smaller distance
between the eo and ei is e', the relationships between e and e' and
the relationships of e/e' are shown in Table 10. When viewing this,
it can be understood that the e and e' are essentially the same at
any zoom position.
Particularly, 0.7<e/e'<1.4 can be satisfied.
Further, when assuming that the backward principal-point position
of the first group G1 is H1', the forward principal-point position
of the third group G3 is H2, the of the entire system is the
smallest in the positive range of the power of the first group G1
at zooming is et1, the distance between the H1' and H2 in a case in
which the power of the entire system is the greatest is ew1, the
distance between the H1' and H2 in a case in which the power of the
entire system is the smallest in the negative range of the power of
the first group G1 at zooming is et2, and the distance between the
H1' and H2 in a case in which the power of the entire system is the
greatest is ew2, it can be understood from FIG. 14 that et1<ew1
et2<ew2 can be satisfied.
With the example 1, the sign of the optical power of the optical
group G4 is substantially unchangeable within the entire zoom
range.
Thus, correction of the residual aberration in the optical groups
G1 and G3 of which optical power is variable, and correction of
aberration fluctuation due to zooming can be performed.
When the maximum value of the absolute value of the optical power
in the optical groups G1 and G3 of which optical power is variable
is |.PHI.d|max at the entire zoom positions, the maximum value of
the absolute value of the optical power in the optical group G4 is
|.PHI.s|max at the entire zoom positions, the condition
|.PHI.s|max<|.PHI.d|max can be satisfied.
This facilitates a predetermined zoom ratio to be readily obtained,
and also reduces the aberration fluctuation caused by zooming.
Also, when assuming that the optical elements E1, E2, E5, and E6
shift, the maximum value of the absolute value of the shift amount
at this time at the entire zoom positions is |Dd|max, and the
maximum value of the absolute value of the shift amount of the
optical element Lss at the entire zoom positions is |Dd|max, the
condition |Ds|max<|Dd|max can be satisfied.
This facilitates a predetermined zoom ratio to be readily obtained,
and also enables the aberration fluctuation accompanied by zooming
to be preferably corrected, in the event that the optical group of
which optical power is variable performs zooming by changing the
optical power.
Note that with the present example and the following examples,
focusing can be performed by moving the entire system, or by moving
one optical group in substantially the vertical direction as to the
optical axis.
Hereinafter, description will be made regarding examples 2 through
4 of at least one exemplary embodiment.
With the examples 2 through 4, description will be made with a
focus on the other features other than the features of the above
example 1.
EXAMPLE 2
FIG. 15 is a lens cross-sectional view according to an example 2 of
at least one exemplary embodiment.
The specifications are substantially similar to example 1. Seven
optical elements (lenses) are employed in total. In order from the
object side, the optical elements E1b, E2b, E5b, and E6b have a
rotational asymmetric shape, these optical elements are decentered
in the Y-axis direction, and the amount of decentering thereof
continuously varies. Also, the absolute value of the amount thereof
is set so as to be equal with mutually positive/negative reverse.
The optical elements E3b and E4b have a rotational symmetric
spherical surface. In the event that an asymmetric aberration
remains on the optical axis, the optical elements E3b and E4b can
have a rotational asymmetric shape to reduce this. The optical
element E7b has a rotational asymmetric shape symmetric as to at
least one surface. This reduces the on-axis coma aberration which
has not been able to be reduced in the optical elements E1b and E2b
by tilting this aberration. Also, the first group G1b comprises the
optical elements E1b and E2b. Similarly, the second group G2b
comprises the optical elements E3b and E4b, and the third group G3b
comprises the optical elements E5b and E6b. As for surface numbers,
the reference plane serving as the origin of the absolute
coordinates system is determined as a surface S0, the first surface
of the optical element E1b is determined as S1b, and in order, the
corresponding surfaces are surfaces S2b, S3b, S4b, and so on, and
following the surface S6b (backward of the optical element E3b) a
diaphragm S7b (SP) is disposed. The first surface of the optical
element E4b is determined as S8b, and the subsequent numbers are
assigned in order, and the image plane IP is S16b. Hereinafter,
decentering continues in the Y-axis direction, and let us say that
the rotational asymmetric groups (G1b and G3b), which contribute to
change in power, the rotational symmetric group (G2b), and the
optical element (E7b) configured to suppress the above residual
aberration by decentering are referred to as decentering movable
blocks, auxiliary block, and auxiliary movable block, respectively.
Disposing the decentering movable blocks G1b and G3b alone makes
the power thereof too strong, and can make it difficult to perform
correction of aberrations, and accordingly, the auxiliary blocks
G2b and E7b are disposed.
The lens data of the example 2 is shown in Table 11. The amount of
shift from the Z axis of the respective optical elements is such as
shown in Table 12, the amount of tilt of the optical element E7b is
such shown in Table 13. The values of the respective coefficients
of the polynomial surfaces represented with Equation 1 are shown in
Tables 14-1 and 14-2. FIG. 16 illustrates the optical path diagrams
at this time in order of a telephoto end T, middle zoom position M,
and wide-angle end W. The optical elements E1b and E2b are
decentered in the Y-axis direction, and the absolute value of the
amount thereof is so as to be equal with mutually positive/negative
reverse, as shown in Table 12. Thus, the power of the first group
G1b is changed from positive to negative between the telephoto end
and the wide-angle end. The ray emitted from the first group G1b
passes through the optical element E3b, diaphragm S7b (SP), and
optical element E4b, and illuminates the optical elements E5b and
E6b. The optical elements E5b and E6b are decentered in the Y-axis
direction, and the absolute value of the amount thereof is so as to
be equal with mutually positive/negative reverse, as shown in Table
10. Thus, the power of the third group G3b is changed from negative
to positive between the telephoto end and the wide-angle end. The
ray passed through these decentering movable blocks illuminates the
next auxiliary block E7b. The auxiliary block E7b compensates the
power necessary for the decentering movable blocks G1b and G3b. The
ray passed through these optical elements forms an image without
changing the image plane IP.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 17A through FIG.
17C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 17A through FIG. 17C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements can be
symmetric as to the X axis, so the positive case should be taken
into consideration regarding the X direction. When viewing the ray
at an angle of view of 0.degree., it can be understood that a coma
aberration can be reduced from the telephoto end to the wide-angle
end. Also, FIG. 18 illustrates the distortion reactor lattices at a
telephoto end T, middle zoom position M, and wide-angle end W. The
lengthwise and crosswise size of the lattices is about 1/4 inch
(vertically 2.7 mm.times.horizontally 3.6 mm). When viewing this
figure, it can be understood that distortion can be suppressed, but
when viewing the ray at an angle of view of 0.degree., it can be
understood that some amount of a coma aberration can remain.
FIG. 19 is a chart plotting change in power .PHI.1 and .PHI.3 of
the first group G1b and the third group G3b, and the sum thereof
.PHI.13 as to the power of the entire system.
At this time, when assuming that the maximum value of the absolute
value of the power in the first group G1b and the third group G3b
is |.PHI.|max, and the power of the sum of the first group G1b and
the third group G3b is .PHI.13, the following condition
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max can be satisfied.
FIG. 20 illustrates change in the principal-point positions before
and after the first group G1b and the third group G3b (H1 is the
forward principal-point position of the first group G1b, H1' is the
backward principal-point position of the first group G1b, H2 is the
forward principal-point position of the third group G3b, and H2' is
the backward principal-point position of the third group G3b). The
first group G1b is made up of meniscus lenses, so the
principal-point position thereof greatly moves. Also, when viewing
the change thereof, it can be understood that the power of the
first group G1b moves in the object direction in the positive range
as the power of the entire system increases, and expands the
interval of the H1 and H2.
Also, when assuming that the forward principal-point position and
the backward principal-point position of the first group G1b are H1
and H1' respectively, the forward principal-point position and the
backward principal-point position of the third group G3b are H2 and
H2' respectively, the distance between the object point and the H1
is eo, the distance between the H1' and H2 is e, the distance
between the H2' and the image point is ei, and smaller distance
between the eo and ei is e', the relationships between e and e' and
the relationships of e/e' are shown in Table 15. When viewing this,
the relationships of e/e' at the telephoto end are as follows
except for a zoom state 4: 0.7<e/e'<1.4
Further, when assuming that the backward principal-point position
of the first group G1b is H1', the forward principal-point position
of the third group G3b is H2, the distance between the H1' and H2
in a case in which the power of the entire system is the smallest
in the positive range of the power of the first group G1b is et1,
the distance between the H1' and H2 in a case in which the power of
the entire system is the greatest is ew1, the distance between the
H1' and H2 in a case in which the power of the entire system is the
smallest in the negative range of the power of the first group G1b
is et2, and the distance between the H1' and H2 in a case in which
the power of the entire system is the greatest is ew2, it can be
understood from FIG. 20 that et1<ew1 et2<ew2 can be
satisfied. The features other than this are substantially similar
to example 1.
EXAMPLE 3
FIG. 21 is a lens cross-sectional view according to an example 3 of
at least one exemplary embodiment.
The specifications of the present example are substantially similar
to example 1. Seven optical elements (lenses) are employed in
total. In order from the object side, the optical elements E1c,
E2c, E5c, and E6c have a rotational asymmetric shape, these optical
elements are decentered in the Y-axis direction, and the amount of
decentering thereof continuously varies. Also, the absolute value
of the amount thereof is set so as to be equal with mutually
positive/negative reverse. The optical elements E3c and E4c have a
rotational symmetric spherical surface. In the event that an
asymmetric aberration remains on the optical axis, the optical
elements E3c and E4c can have a rotational asymmetric shape to
reduce this. The optical element E7c also has a rotational
symmetric shape. This reduces the on-axis coma aberration which may
not have been reduced in the optical elements E1c and E2c by
shifting this aberration. Also, the first group G1c comprises the
optical elements E1c and E2c. Similarly, the second group G2c
comprises the optical elements E3c and E4c, and the third group G3c
comprises the optical elements E5c and E6c. As for surface numbers,
the reference plane serving as the origin of the absolute
coordinates system is determined as a surface S0, the first surface
of the optical element E1c is determined as S1c, and in order, the
corresponding surfaces are S2c, S3c, S4c, and so on, and following
the surface S6c (backward of the optical element E3c) a diaphragm
S7c (SP) is disposed. The first surface of the optical element E4
is determined as S8c, and the subsequent numbers are assigned in
order, and the image plane IP is S16c. Hereinafter, decentering
continues in the Y-axis direction, and let us say that the
rotational asymmetric groups (G1c and G3c), which contribute to
change in power, the rotational symmetric group (G2c), and the
optical element (E7c) configured to suppress the above residual
aberrations by decentering are referred to as decentering movable
blocks, auxiliary block, and auxiliary movable block, respectively.
Disposing the decentering movable blocks G1c and G3c alone makes
the power thereof too strong, and can make it difficult to perform
correction of an aberration, and accordingly, the auxiliary blocks
G2c and E7c are disposed.
The lens data of the example 3 is shown in Table 16. The amount of
shift from the Z axis of the respective optical elements is such as
shown in Table 17, and the amount of shift of the optical element
E7 is such as shown in Table 18. The values of the respective
coefficients of the polynomial surfaces represented with Equation 1
are shown in Table 19. FIG. 22 illustrates the optical path
diagrams at this time in order of a telephoto end T, middle zoom
position M, and wide-angle end W. The lenses of the optical
elements E1c and E2c are decentered in the Y-axis direction, and
the absolute value of the amount thereof is so as to be equal with
mutually positive/negative reverse, as shown in Table 17. Thus, the
power of the first group G1c is changed from positive to negative
between the telephoto end and the wide-angle end. The ray emitted
from the first group G1c passes through the optical element E3c,
diaphragm S7c (SP), and optical element E4c, and illuminates the
optical elements E5c and E6c. The optical elements E5c and E6c are
decentered in the Y-axis direction, and the absolute value of the
amount thereof is so as to be equal with mutually positive/negative
reverse, as shown in Table 17. Thus, the power of the third group
G3c is changed from negative to positive between the telephoto end
and the wide-angle end. The ray passed through these decentering
movable blocks illuminates the next auxiliary block E7c. The
auxiliary block E7c compensates the power necessary for the
decentering movable blocks G1c and G3c. The ray passed through
these optical elements forms an image without changing the image
plane IP.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 23A through FIG.
23C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 23A through FIG. 23C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X axis, so only the positive case should be
taken into consideration regarding the X direction. When viewing
the ray at an angle of view of 0.degree., it can be understood that
a coma aberration can be reduced from the telephoto end to the
wide-angle end. Also, FIG. 24 illustrates the distortion reactor
lattices at a telephoto end T, middle zoom position M, and
wide-angle end W. The lengthwise and crosswise size of the lattices
is about 1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm).
When viewing this figure, it can be understood that distortion can
be suppressed, but when viewing the ray at an angle of view of
0.degree., it can be understood that some amount of a coma
aberration can remain.
FIG. 25 is a chart plotting change in power .PHI.1 and .PHI.33 of
the first group G1c and the third group G3c, and the sum thereof
.PHI.13 as to the power of the entire system.
At this time, when assuming that the maximum value of the absolute
value of the power in the first group G1c and the third group G3c
is .PHI.10, max, and the power of the sum of the first group G1c
and the third group G3c is (.PHI.13, the following condition
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max can be satisfied.
FIG. 26 illustrates change in the principal-point positions before
and after the first group G1c and the third group G3c (H1 is the
forward principal-point position of the first group G1c, H1' is the
backward principal-point position of the first group G1c, H2 is the
forward principal-point position of the third group G3c, and H2' is
the backward principal-point position of the third group G3c). The
first group G1c is made up of meniscus lenses, so the
principal-point position thereof greatly moves. Also, when viewing
the change thereof, it can be understood that the power of the
first group G1c moves in the object direction in the positive range
as the power of the entire system increases, and expands the
interval of the H1 and H2. Also, it can be understood that the
power of the first group G1c moves in the object direction even in
the negative range as the power of the entire system increases, and
expands the interval of the H1 and H2. Also, when assuming that the
forward principal-point position and the backward principal-point
position of the first group G1c are H1 and H1' respectively, the
forward principal-point position and the backward principal-point
position of the third group G3c are H2 and H2' respectively, the
distance between the object point and the H1 is eo, the distance
between the H1' and H2 is e, the distance between the H2' and the
image point is ei, and smaller distance between the eo and ei is
e', the relationships between e and e' and the relationships of
e/e' are shown in Table 20. When viewing this, the following
condition 0.7<e/e'<1.4 can be satisfied except for a zoom
state 5.
Further, when assuming that the backward principal-point position
of the first group G1c is H1', the forward principal-point position
of the third group G3c is H2, the distance between the H1' and H2
in a case in which the power of the entire system is the smallest
in the positive range of the power of the first group G1c is et1,
the distance between the H1' and H2 in a case in which the power of
the entire system is the greatest is ew1, the distance between the
H1' and H2 in a case in which the power of the entire system is the
smallest in the negative range of the power of the first group G1c
is et2, and the distance between the H1' and H2 in a case in which
the power of the entire system is the greatest is ew2, it can be
understood from FIG. 26 that et1<ew1 et2<ew2 can be
satisfied.
The features other than this are substantially similar to example
1.
EXAMPLE 4
FIG. 27 is a lens cross-sectional view according to an example 4 of
at least one exemplary embodiment.
The specifications are substantially similar to example 1. Seven
optical elements (lenses) are employed in total. In order from the
object side, the optical elements E1d, E2d, E5d, and E6d have a
rotational asymmetric shape, these optical elements are decentered
in the Y-axis direction, and the amount of decentering thereof
continuously varies. Also, the absolute value of the amount thereof
is set so as to be equal with mutually positive/negative reverse.
The optical elements E3d and E4d have a rotational symmetric
spherical surface. In the event that an asymmetric aberration
remains on the optical axis, the optical elements E3d and E4d can
have a rotational asymmetric shape to reduce this. The optical
elements E7d and E8d have a rotational asymmetric shape symmetric
as to at least one surface. This reduces the on-axis coma
aberration which has not been able to be reduced in the optical
elements E1d and E2d by tilting this aberration. Also, the first
group G1d comprises the optical elements E1d and E2d. Similarly,
the second group G2d comprises the optical elements E3d and E4d,
the third group G3d comprises the optical elements E5d and E6d, and
the fourth group G4d comprises the optical elements E7d and E8d. As
for surface numbers, the reference plane serving as the origin of
the absolute coordinates system is determined as a surface S0, the
first surface of the optical element E1d is determined as S1d, and
in order, the corresponding surfaces are S2d, S3d, S4d, and so on,
and following the surface S6d (backward of the optical element E3d)
a diaphragm S7d (SP) is disposed. The first surface of the optical
element E4d is determined as S8d, and the subsequent numbers are
assigned in order, and the image plane IP is S18d. Hereinafter,
decentering continues in the Y-axis direction, and let us say that
the rotational asymmetric groups (G1d and G3d), which contribute to
change in power, the rotational symmetric group (G2d), and the
group (G4d) configured to suppress the above residual aberrations
by decentering are referred to as decentering movable blocks,
auxiliary block, and auxiliary movable block, respectively.
Disposing the decentering movable blocks G1d and G3d alone makes
the power thereof too strong, and can make it difficult to perform
correction of aberrations, and accordingly, the auxiliary block G2d
is disposed.
The lens data of the example 4 is shown in Table 21. Table 22 shows
the amount of shift from the Z axis of the respective optical
elements, and Table 23 shows the amount of tilt in the optical
elements E7d and E8d. The values of the respective coefficients of
the polynomial surfaces represented with Equation 1 are shown in
Table 24. FIG. 28 illustrates the optical path diagrams at this
time in order of a telephoto end T, middle zoom position M, and
wide-angle end W. The optical elements E1d and E2d are decentered
in the Y-axis direction, and the absolute value of the amount
thereof is so as to be equal with mutually positive/negative
reverse, as shown in Table 22. Thus, the power of the first group
G1d is changed from positive to negative between the telephoto end
and the wide-angle end. The ray emitted from the first group G1d
passes through the optical element E3d, diaphragm S7 (SP), and
optical element E4d, and illuminates the optical elements E5d and
E6d. The optical elements E5d and E6d are decentered in the Y-axis
direction, and the absolute value of the amount thereof is so as to
be equal with mutually positive/negative reverse, as shown in Table
22. Thus, the power of the third group G3d is changed from negative
to positive between the telephoto end and the wide-angle end. The
ray passed through these decentering movable blocks illuminates the
next auxiliary block G4d. The auxiliary block G4d compensates the
power necessary for the decentering movable blocks. The ray passed
through these optical elements forms an image without changing the
image plane.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 29A through FIG.
29C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 29A through FIG. 29C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements can be
symmetric as to the X axis, so the positive case should be taken
into consideration regarding the X direction. When viewing the ray
at an angle of view of 0.degree., it can be understood that a coma
aberration can be reduced from the telephoto end to the wide-angle
end. Also, FIG. 30 illustrates the distortion reactor lattices at a
telephoto end T, middle zoom position M, and wide-angle end W. The
lengthwise and crosswise size of the lattices is about 1/4 inch
(vertically 2.7 mm.times.horizontally 3.6 mm). When viewing this
figure, it can be understood that distortion can be suppressed, but
when viewing the ray at an angle of view of 0.degree., it can be
understood that some amount of a coma aberration can remain.
FIG. 31 is a chart plotting change in power .PHI.1 and .PHI.3 of
the first group G1d and the third group G3d, and the sum thereof
.PHI.13 as to the power of the entire system.
At this time, when assuming that the maximum value of the absolute
value of the power in the first group G1d and the third group G3d
is |.PHI.|max, and the power of the sum of the first group G1d and
the third group G3d is .PHI.13, the following condition
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max can be satisfied.
FIG. 32 illustrates change in the principal-point positions before
and after the first group G1d and the third group G3d (H1 is the
forward principal-point position of the first group G1d, H1' is the
backward principal-point position of the first group G1d, H2 is the
forward principal-point position of the third group G3d, and H2' is
the backward principal-point position of the third group G3d). The
first group G1d is made up of meniscus lenses, so the
principal-point position thereof greatly moves. Also, when viewing
the change thereof, it can be understood that the power of the
first group G1d moves in the object direction in the positive range
as the power of the entire system increases, and expands the
interval of the H1 and H2. Also, it can be understood that the
power of the first group G1d moves in the object direction even in
the negative range as the power of the entire system increases, and
expands the interval of the H1 and H2. Also, when assuming that the
forward principal-point position and the backward principal-point
position of the first group G1d are H1 and H1' respectively, the
forward principal-point position and the backward principal-point
position of the third group G3d are H2 and H2' respectively, the
distance between the object point and the H1 is eo, the distance
between the H1' and H2 is e, the distance between the H2' and the
image point is ei, and smaller distance between the eo and ei is
e', the relationships between e and e' and the relationships of
e/e' are shown in Table 25. When viewing this, the following
condition 0.7<e/e'<1.4 can be satisfied except for a zoom
state 5.
Further, when assuming that the backward principal-point position
of the first group G1d is H1', the forward principal-point position
of the third group G3d is H2, the distance between the H1' and H2
in a case in which the power of the entire system is the smallest
in the positive range of the power of the first group G1d is et1,
the distance between the H1' and H2 in a case in which the power of
the entire system is the greatest is ew1, the distance between the
H1' and H2 in a case in which the power of the entire system is the
smallest in the negative range of the power of the first group G1d
is et2, and the distance between the H1' and H2 in a case in which
the power of the entire system is the greatest is ew2, it can be
understood from FIG. 32 that et1<ew1 et2<ew2 can be
satisfied.
The features other than this are substantially similar to example
1.
As described above, according to the respective examples, zooming
can be performed while preferably eliminating an aberration by
moving the rotational asymmetric optical elements in the direction
different from the optical axis, and also a compact optical system
having excellent optical capabilities can be obtained.
EXAMPLE 5
FIG. 33 is a lens cross-sectional view according to an example 5 of
at least one exemplary embodiment.
In FIG. 33, T, M, and W are lens cross-sectional views at the
telephoto end (the zoom position where the power of the entire
system is the minimum), at a middle zoom position, and at the
wide-angle end (the zoom position where the power of the entire
system is the maximum) respectively.
FIG. 34 is a lens cross-sectional view for selecting the middle
zoom position of the example 5 in FIG. 33 (M in FIG. 33) as an
example and describing respective factors.
A zoom optical system according to the example 5 is a photography
lens system employed for an imaging apparatus, and the left hand is
the object side, and the right hand is the image side in the lens
cross-sectional view.
Note that the zoom optical system according to the example 5 can be
employed as a projector, and in this case, the left hand is a
screen, and the right hand is a projection surface.
In FIG. 33 and FIG. 34, G1e and G2e are optical groups of which
optical power is variable.
G3e is an optical group having symmetry as to at least one surface,
and including one or more optical elements Ls capable of
decentering.
Zooming is performed by changing the power in the two optical
groups G1e and G2e each of which optical power is variable.
The two optical groups G1e and G2e each of which optical power is
variable each include a rotationally asymmetrical surface, move in
the direction different from the optical axis, and include two
optical elements E1e and E2e which change the power within the
optical group G1e, and two optical elements E3e and E4e which
change the power within the optical group G2e, respectively.
Note that the term "optical power" refers to the power of a surface
positioned on the optical axis, and when the surface on the optical
axis varies by the optical element having a rotationally
asymmetrical surface being decentered, optical power is also
changed in response to that change.
With the example 5 of at least one exemplary embodiment, five
optical elements (lenses) are employed in total. In order from the
object side, the optical elements E1e, E2e, E3e, and E4e have a
rotational asymmetric shape, these optical elements are decentered
in the Y-axis direction, and the amount of decentering continuously
varies. The optical element E5e has a rotational asymmetric shape
symmetric as to at least one surface. This reduces the on-axis coma
aberration which may not have been reduced in the optical elements
E1e through E4e by shifting or tilting this aberration. Also, the
first group G1e comprises the optical elements E1e and E2e.
Similarly, the second group G2e comprises the optical elements E3e
and E4e, and the third group G3e comprises the optical element E7e.
As for surface numbers, the reference plane serving as the origin
of the absolute coordinates system is determined as a surface S0,
the first surface of the optical element E1e is determined as S1e,
and in order, the corresponding surfaces are surfaces S2e, S3e, and
S4e, and following the surface S4e (backward of the optical element
E2e) a diaphragm S5e (SP) is disposed. The first surface of the
optical element E3e is determined as S6e, and the subsequent
numbers are assigned in order, and the image plane IP is S12e.
Hereinafter, decentering continues in the Y-axis direction, and let
us say that the rotational asymmetric groups (G1e and G2e), which
contribute to change in power, and the third group G3e made up of
the optical element (E5e) configured to suppress the above residual
aberrations by decentering are referred to as decentering movable
blocks G1e and G2e, and auxiliary movable block G3,
respectively.
The lens data of the example 5 is shown in Table 26. The amount of
shift from the Z axis of the respective optical elements is shown
in Table 27. The values of the respective coefficients of the
polynomial surfaces represented with Equation 1 are shown in Tables
28-1 and 28-2. The optical elements E1e and E2e are decentered in
the Y-axis direction. Thus, the power of the first group G1e is
changed from positive to negative between the telephoto end and the
wide-angle end. The ray emitted from the first group G1e passes
through the diaphragm SP, and illuminates the optical elements E3e
and E4e. The optical elements E3e and E4e are decentered in the
Y-axis direction. Thus, the power of the second group G2e is
changed from negative to positive between the telephoto end and the
wide-angle end. The ray passed through these decentering movable
blocks G1e and G2e illuminates the next auxiliary movable block
G3e. The auxiliary movable block G3e compensates the power
necessary for the decentering movable blocks G1e and G2e. The ray
passed through these optical elements forms an image without
changing the image plane IP.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 35A through FIG.
35C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 35A through FIG. 35C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X axis, so only the positive case should be
taken into consideration regarding the X direction. When viewing
the ray at an angle of view of 0.degree., it can be understood that
a coma aberration can be reduced from the telephoto end to the
wide-angle end. Also, FIG. 36 illustrates the distortion reactor
lattices at a telephoto end T, middle zoom position M, and
wide-angle end W. The lengthwise and crosswise size of the lattices
is about 1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm).
When viewing this figure, it can be understood that distortion can
be suppressed, but when viewing the ray at an angle of view of
0.degree., it can be understood that some amount of a coma
aberration can remain. Table 29 shows comparisons of the power in
the first group G1e and third group G3e in the above design
example, and the examples 1 through 5 (the first group G1e and
second group G2e in the example 5), and the auxiliary movable block
(E7a-c in the examples 1 through 3, G4d in the example 4, and E5e
in the example 5). The shaded portions show the maximum value of
the absolute value of the auxiliary movable block and the
decentering movable block (|.PHI.s|max and |.PHI.d|max,
respectively).
When comparing these, it can be understood that change in power of
the auxiliary movable block does not include change in
positive/negative, and the absolute value |.PHI.s|max of the
maximum value of the power of the auxiliary movable block is
smaller than the |.PHI.d|max of the decentering movable block in
any embodiment. In other words, |.PHI.s|max<|.PHI.d|max
holds.
Further, when assuming that the absolute value of the value
obtained by subtracting the minimum value from the maximum value of
the power of the decentering auxiliary block straddle the entire
zoom area is .DELTA.|.PHI.s|, .DELTA.|.PHI.s|<0.1 holds, and
when assuming that the absolute value of the value obtained by
subtracting the minimum value from the maximum value of the power
of the auxiliary movable block straddle the entire zoom area is
.DELTA.|.PHI.d|, .DELTA.|.PHI.d|>0.5 holds. When comparing
.DELTA.|.PHI.d| between the G1a-d and G3a-d, and assuming that the
smaller one is determined as .DELTA.|.PHI.d|min,
.DELTA.|.PHI.d|min/.DELTA.|.PHI.d|>6 holds, and also
.DELTA.|.PHI.d|min/.DELTA.|.PHI.d|>25 holds except for the
example 5. Accordingly, it can be understood from comparison
between aberration charts that the auxiliary movable block does not
affect upon the power fluctuation of the entire system, and relates
to elimination of a on-axis coma aberration.
Note that with the above respective examples, three or more optical
groups of which optical power is variable can be employed. Also,
two or more optical groups having symmetry as to at least one
surface, and including one or more optical elements capable of
decentering can be employed.
Also, optical groups of which optical power is substantially
unchangeable can be omitted, or two or more optical groups of which
optical power is variable can be employed.
Next, an example of a digital still camera (imaging apparatus) to
which a zoom optical system according to at least one exemplary
embodiment can be applied as a photographic optical system will be
described with reference to FIG. 37.
In FIG. 37, reference numeral 20 denotes a camera body, 21 denotes
a photographic optical system made up of a zoom optical system
according to at least one exemplary embodiment, 22 denotes a
solid-state imaging device (photoelectric conversion element) such
as a CCD sensor or CMOS sensor which receives a subject image using
the photographic optical system 21, 23 denotes memory for recording
the subject image photo-accepted by the imaging device 22, and 24
denotes a finder for observing the subject image displayed on an
unshown display element.
The above display element is made up of a liquid crystal panel or
other related or equivalent display apparatus as known by one of
ordinary skill in the relevant art, on which the subject image
formed on the imaging device 22 is displayed.
Thus, the present example realizes an imaging apparatus which is
small and has high optical capabilities by applying the zoom
optical system according to the present example to the imaging
apparatus such as a digital still camera. It is needless to say
that as for the zoom optical system to be applied to this imaging
apparatus, the zoom optical system according to any one of not the
above examples 1 through 5 but also later-described examples 6 and
7 can be employed.
COMPARATIVE EXAMPLE 1
Next, a comparative example 1 of at least one exemplary embodiment
will be shown. The comparative example 1 has been designed with
reference to Japanese Patent Laid-Open No. 1990-119103. FIG. 4
illustrates a lens cross-sectional view of the comparative example
1.
The zoom optical system according to the comparative example 1 is
made up of two optical groups G1f and G2f each including two
rotational asymmetric optical elements as illustrated in FIG. 4,
which are referred to as the first group G1f, and the second group
G2f in order from the object side. This first group G1f comprises
optical elements E1f and E2f, and the second group G2f comprises
optical elements E3f and E4f. First, a paraxial calculation is
performed by approximating these groups using one thin-thickness
lens. Next, let us say that the power of the thin-thickness lens of
the first group G1f and the power of the thin-thickness lens of the
second group G2f are .PHI.1 and .PHI.2 respectively, and a
principal interval and back focus are e and Sk respectively. Also,
when assuming that the power of the entire system is .PHI., and the
focal distance is f, the following equation holds.
.PHI..PHI..PHI..times..times..PHI..times..PHI..times..times.
##EQU00001##
Also, as for the back focus Sk, the following equation holds from
the paraxial calculation.
.times..times..PHI..PHI..times..times. ##EQU00002##
Here, if the principal-point interval e and the back focus Sk are
determined, the power .PHI.1 and .PHI.2 are represented as the
function of the power .PHI. of the entire system from Equations 6
and 7. That is to say, the track of change in power in the first
group G1f and second group G2f according to change in power of the
entire system can be represented. Accordingly, when assuming that
the principal-point interval e=3, and the back focus Sk=15, the
power .PHI.1 and .PHI.2 are as follows:
.PHI..times..phi..times..times..PHI..times..phi..times..times.
##EQU00003##
Upon the relationships of the power .PHI.1 and .PHI.2 as to the
power .PHI. of the entire system being represented with a graph,
the graph such as illustrated in FIG. 3 will be obtained. When
viewing this, it can be understood that as the power .PHI. of the
entire system increases, the power of the first group G1f changes
to negative from positive, and inversely, the power of the second
group G2f changes to positive from negative. Here, a rotational
asymmetric curved surface is represented with Equation 10, and the
relationships between the coefficient thereof "a" and the power
results in Equation 11. z=ay.sup.3+3ax.sup.2y [Equation 10]
.PHI.=12a.delta.(n-1) [Equation 11]
Here, x, y, and z are the above axes. .delta. is the amount of
shift toward the Y-axis direction from the Z axis of the two
rotational asymmetric optical elements E1f and E2f (E3f and E4f),
and n is the refractive index of the lens. The coefficients a and n
of the rotational asymmetric optical elements E1f through E4f are
shown in Table 1, in which the amount of shift .delta. from the z
axis is also shown in order of the telephoto end, middle zoom
position, and wide-angle end. Also, Table 2 shows the surface-types
of the respective surfaces S0 through S9f, and surface
intervals.
In FIG. 4, the ray illuminated a reference plane S0 first
illuminates the first group G1f. Let us say that the first group
G1f is made up of the two optical elements (lenses) E1f and E2f,
and the surface numbers are S1f through S4f in order. The optical
elements E1f and E2f are decentered in the Y-axis direction, and
the amount of decentering continuously varies. Also, the absolute
value of the amount thereof is set so as to be equal with mutually
positive/negative reverse. This causes the power .PHI.1 of the
first group G1f to be changed from positive to negative at the time
of zooming from the telephoto end to the wide-angle end
(hereinafter, the zoom direction is the same) such as illustrated
in FIG. 3. The ray emitted from the first group G1f next passes
through the diaphragm S5f, and illuminates the second group G2f.
Let us say that the second group G2f, as with the first group G1f,
comprises two optical elements E3f and E4f, and the surface numbers
thereof are S6f through S9f. The optical elements E3f and E4f are
decentered in the Y-axis direction, and the amount of decentering
continuously varies. Also, the absolute value of the amount thereof
is set so as to be equal with mutually positive/negative reverse.
This causes the power .PHI.2 of the second group G2f to be changed
from negative to positive such as illustrated in FIG. 3.
The ray passed through these groups G1f and G2f forms an image
without changing the image plane IP. However, when viewing the
image plane, it can be understood that the image is formed, but an
aberration greatly occurs. This occurs regardless of the paraxial
allocations determined with Equations 8 and 9. For example, a coma
aberration which occurs on the axis cannot be reduced with paraxial
allocations alone anyway. As the above result, it can be understood
that with the comparative example, an aberration cannot be
completely corrected in the following points. This is caused by (a)
an optical system having rotational asymmetric optical elements is
asymmetric as to the optical axis, so shift is caused upon the
upper line and underline, and consequently, a coma aberration
occurs event on the marginal ray, and (b) curvature of field
occurs.
Accordingly, with the examples of at least one exemplary
embodiment, a zoom optical system capable of sufficiently
eliminating an aberration is realized by moving the optical element
(lens) in the direction different from the optical axis to perform
zooming.
COMPARATIVE EXAMPLE 2
Next, a comparative example 2 of at least one exemplary embodiment
will be described.
Generally, if eliminating a coma aberration on the marginal ray and
increasing the power of a decentering movable block (also referred
to as optical power which is the inverse number of a focal
distance) can be achieved contemporaneously, a zoom optical system
with high precision and a high zoom ratio can be achieved. However,
generally, upon increasing the power of a decentering movable
block, the tilt of each surface is also increased, and
consequently, it becomes difficult to suppress on-axis coma
aberration. Accordingly, with at least one exemplary embodiment,
correction of power is performed by disposing a coaxial lens
(coaxial optical element) within an optical path to suppress the
power of the decentering movable block, thereby suppressing an
on-axis coma aberration.
With the comparative example 2 of at least one exemplary
embodiment, the optical element E7a-d of the fourth group G4a-d
according to the examples 1 through 4 comprises one optical element
made up of a rotational symmetric sphere, which is fixed at the
time of zooming (not decentered in the optical-axis direction).
Next, description will be made regarding the optical capabilities
of the comparative example 2 at this time.
FIG. 2 is a lens cross-sectional view at the middle zoom position
of the comparative example 2. FIG. 5 is an optical-path diagram
according to a comparative example 2 of at least one exemplary
embodiment. With the comparative example 2, let us say that a CCD
is employed as an imaging surface, and the size thereof is about
1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm). Also, the
incident pupil diameter is assumed to be about 0.8. The number of
optical elements (lenses) are seven in total, in order from the
object side to the image side, the optical elements E1g, E2g, E5g,
and E6g have a rotational asymmetric shape, these optical elements
are decentered in the Y-axis direction, and the amount of
decentering thereof continuously varies. Also, the absolute value
of the amount thereof is set so as to be equal with mutually
positive/negative reverse. The optical elements E3g, E4g, and E7g
have a rotational symmetric spherical shape, but in the event that
an asymmetric aberration remains on the optical axis, optical
elements having a rotational asymmetric shape can be disposed to
reduce this. Also, the first group G1g comprises the optical
elements E1g and E2g.
Similarly, the second group G2g comprises the optical elements E3g
and E4g, and the third group G3g comprises the optical elements E5g
and E6g. As for surface numbers, the reference plane serving as the
origin of the absolute coordinates system is determined as a
reference plane S0, the first surface of the optical element E1g is
determined as S1g, and in order, the corresponding surfaces are
S2g, S3g, S4g and so on, and following the surface S6g (backward of
the optical element E3g) a diaphragm SP is disposed, which is
determined as S7g. The first surface of the optical element E4g is
determined as S8g, and the subsequent numbers are assigned in
order, and the image plane IP is S16g. Hereinafter, let us say that
the rotational asymmetric groups (group G1g and group G3g), which
are continuously decentered in the Y-axis direction, and the
rotational symmetric groups (group G2g and optical element E7g) are
referred to as decentering movable blocks and auxiliary blocks.
Disposing the decentering movable blocks G1g and G3g alone makes
the power thereof too strong, and can make it difficult to perform
correction of an aberration, and accordingly, the auxiliary blocks
G2g and E7g are disposed.
The lens data of the comparative example 2 is shown in Table 3. The
amount of shift from the Z axis (optical axis) of the respective
optical elements (lenses) is such as shown in Table 4, and the
values of the respective coefficients of the polynomial surfaces
represented with Equation 1 is shown in Table 5. The optical-path
diagram at this time is shown in FIG. 6 in order of the telephoto
end, middle, and wide-angle end. The optical elements E1g and E2g
are decentered in the Y-axis direction, and the absolute value of
the amount thereof is so as to be equal with mutually
positive/negative reverse, as shown in Table 4. This causes the
power of the first group G1g to be changed from positive to
negative. The ray emitted from the first group G1g passes through
the optical element E3g, diaphragm S7g, and optical element E4g,
and illuminates the optical elements E5g and E6g. The optical
elements E5g and E6g are decentered in the Y-axis direction, and
the absolute value of the amount thereof is so as to be equal with
mutually positive/negative reverse, as shown in Table 4. This
causes the power of the G3g to be changed from negative to
positive. The ray passed through these decentering movable blocks
G1g and G3g illuminates the next auxiliary block E7g. The auxiliary
block E7g compensates the power necessary for the decentering
movable blocks G1g and G3g. The ray passed through these optical
elements forms an image without changing the image plane at the
time of zooming.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 7A through FIG. 7C,
respectively. The horizontal axis represents the position of a ray
on the pupil, and the vertical axis represents the shift from the
chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 7A through FIG. 7C are
angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X-axis direction, so only the positive case
should be taken into consideration regarding the X direction. When
viewing the ray at an angle of view of 0.degree., it can be
understood that a coma aberration can be reduced from the telephoto
end to the wide-angle end. Also, FIG. 9 illustrates the distortion
reactor lattices at a telephoto end T, middle zoom position M, and
wide-angle end W. The lengthwise and crosswise size of the lattices
is about 1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm).
When viewing this figure, it can be understood that distortion can
be suppressed, but when viewing the ray at an angle of view of
0.degree., it can be understood that some amount of a coma
aberration can remain.
This is because when moving the decentering movable blocks G1g and
G3g, the angle as to the ray of the surface varies as the optical
power of the entire system varies, so the aberration has not been
completely corrected. Accordingly, in order to reduce this, at
least one exemplary embodiment is directed to another correction
block for correcting and/or reducing angle of a marginal ray to be
changed along with the movement of the decentering movable blocks
G1g and G3g.
That is to say, with at least one exemplary embodiment, a zoom
optical system comprising multiple optical groups G1g and G3g made
up of multiple optical elements each having a rotationally
asymmetrical surface, and changing optical power by the optical
elements E1g and E2g (E5g and E6g) within the respective groups G1g
(G3g) of the multiple optical groups moving mutually in the
direction different from the optical axis, which provides at least
one optical element (auxiliary movable block) E7g having symmetry
as to at least one surface for decentering to reduce the residual
aberration of the zoom optical system. Further, the auxiliary
movable block E7g is disposed to reduce the residual aberration, so
the power and the amount of decentering are less than those in the
decentering movable blocks G1g and G3g. Accordingly, the auxiliary
movable block E7g has no change in positive/negative refracting
power, and further, is arranged so as to satisfy the following
conditions when assuming that the maximum value of the absolute
value of the optical power in the decentering movable blocks G1g
and G3g is |.PHI.d|max, and the maximum value of the absolute value
of the optical power in the auxiliary movable block is |.PHI.s|max.
|.PHI.s|max<|.PHI.d|max [Equation 12]
Further, when assuming that the absolute value of the value
obtained by subtracting the minimum value from the maximum value of
the power of the decentering auxiliary block straddle the entire
zoom area is .DELTA.|.PHI.s|, the following range can be satisfied.
.DELTA.|.PHI.s|<0.2 Or in at least one exemplary embodiment,
.DELTA.|.PHI.s<0.1
Upon exceeding this range, the asymmetric aberration, i.e., the
features of the decentering auxiliary block are reduced, and this
block results in being classified as a decentering movable
block.
Also, when assuming that the absolute value of the value obtained
by subtracting the minimum value from the maximum value of the
power in the auxiliary movable block straddle the entire zoom area
is .DELTA.|.PHI.d|, the following range can be satisfied.
.DELTA.|.PHI.d|<0.2 Or in at least one exemplary embodiment,
.DELTA.|.PHI.d|<0.5
Upon exceeding this range, the asymmetric aberration, i.e., the
features of the decentering movable block are reduced, and this
block results in being classified as a decentering auxiliary
block.
Further, when assuming that .DELTA.|.PHI.d| is compared with the
G1g and G3g, and the smaller one is taken as .DELTA.|.PHI.d|min,
the following range can be satisfied.
.DELTA.|.PHI.d|min/.DELTA.|.PHI.d|>6 or in at least one
exemplary embodiment, .DELTA.|.PHI.d|min/.DELTA.|.PHI.d|>25
This is caused by the same reason as the above. Also, in the event
of the auxiliary movable block E7g performing aid with shift, when
assuming that the maximum value of the absolute value of the amount
of shift (amount of movement) thereof is |Ds|max, and the maximum
value of the absolute value of the amount of shift of the
decentering movable block is |Dd|max, the following condition can
be satisfied. |Ds|max<|Dd|max [Equation 13]
Further, it has been known that if the Petzval is great, the
curvature of field also becomes great, and if the Petzval is small,
the curvature of field also becomes small. Accordingly, at least
one exemplary embodiment suppresses the curvature of field to small
by reducing the Petzval. When the power at lenses Ei (i=1 through
n) is .PHI.Ei, and the refractive index of a material is nEi, the
Petzval is obtained with the following equation. PEi=.PHI.Ei/nEi
[Equation 14]
With a normal zoom optical system using a coaxial optical element,
this value can be constant. However, with an optical system such as
in at least one exemplary embodiment where an optical element is
continuously decentered, and power varies, this value is not
constant. Also, the refractive index of a nitrifying material is
around 1.45 through 1.9, so change thereof is small, and
accordingly, change in the Petzval can be referred to change in
power. Accordingly, in order to suppress this Petzval, when
assuming that the maximum value of the absolute value of the power
in the first group G1g and the third group G3g is |.PHI.|max, and
the power in total of the first group G1g and the third group G3g
is .PHI.13, the range of change in power is determined so as to
satisfy the following equation.
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max [Equation 15]
Next, description will be made from the perspective of a
principal-point position.
In order to perform zooming while maintaining compactness, it can
be necessary in some circumstances to move a principal-point
position greatly from a certain position of each group. With the
conventional optical system in which a tertiary curve is simply
given to a single surface, a principal-point position exists only
upon the surface with the tertiary coefficient thereof, and does
not fluctuate greatly. As for a method for fluctuating a
principal-point position greatly, for example, an arrangement can
be made where curvature is given to a single surface, and the shape
of a rotational asymmetric lens is changed into a meniscus shape.
The lens which can have a meniscus shape, which is different from a
positive lens and a negative lens, is a lens capable of disposing a
principal point outside of the lens, and employing this shape for
the rotational asymmetric lens enables a principal point to be
greatly fluctuated outside of the group. However, when making the
rotational asymmetric lens into a meniscus shape, shifting occurs
upon the upper line and underline of the marginal ray at the
telephoto end or the wide-angle end (when the ray passes through
the end of the lens). Accordingly, it is useful for another lens to
correct this. With a method for solving this, the lens for
correction is changed into a meniscus shape having a reverse tilt
to cancel out the shift of the upper line and underline. A
coefficient is determined by focusing attention on this at the time
of introducing a higher order coefficient than a tertiary
coefficient. Also, a meniscus shape can be shaped in the direction
for reducing the mutual distance. This is because reducing the
distance between the lenses enables a on-axis coma aberration to be
reduced while suppressing this to the minimum upon each surface.
Thus, on-axis coma aberration can be reduced.
With the comparative example 2, elimination of a on-axis coma
aberration is performed by obtaining Equations 6 through 9, and
obtaining change in power of each group as to the focal distance as
illustrated in FIG. 3. Upon increasing the power of each group, an
aberration occurs, so in order to increase a variable power ratio
without increasing the power of each group, it can be necessary in
some circumstances to reduce the tilt of change in power of each
group as to the power of the entire system shown in FIG. 3. Thus,
the range of change in power of the entire system can be expanded
while maintaining the range of change in power of each group in a
steady manner. Here, in order to realize the above, paraxial
allocations for performing thin-thickness approximation will be
reconsidered. The following equations can be derived from Equations
6 and 7 with the back focus Sk and the principal-point interval e
serving as variables. However, the respective paraxial values of
the focal distance, forward principal-point position, and backward
principal-point position can be defined as values derived from
Optics Vol. 29, No. 3 (2000). Deriving these values is performed by
calculating 4.times.4 determinants based on the curvature of each
surface and each surface interval.
.PHI..times..PHI..times..times..PHI..times..times..times..PHI..times..tim-
es..times..times..times..times..times..times. ##EQU00004##
It can be understood from the above equations that the tilts of the
two can be determined by the principal-point interval e and the
back focus Sk. Consequently, the following equations are derived by
differentiating the two with the power .PHI..
d.PHI.d.PHI..times..times.d.PHI.d.PHI..times..times..times..PHI..times..t-
imes..times..times..times..times. ##EQU00005##
The power .PHI.1 varies in a linear curve, so the tilt thereof is
constant. On the other hand, the tilt of the power .PHI.1 varies
depending on the power .PHI. of the entire system. Also, if the
principal-point interval e increases, the tilts of the power .PHI.1
and .PHI.2 decrease to realize large magnification, but if the back
focus Sk increases, the power .PHI.1 increases, on the other hand
the power .PHI.2 decreases, and consequently, the direction of
change in the back focus Sk as to large magnification cannot be
determined.
Here, the tilts of the power .PHI.1 and .PHI.2 as to change in the
power .PHI. of the entire system are compared. At a point of
.PHI..times..times. ##EQU00006## in which .PHI.2=0 holds,
d.PHI.d.PHI.d.PHI.d.PHI..times..times..times..times. ##EQU00007##
holds, in the range of
.PHI.<.times..times.d.PHI.d.PHI.<d.PHI.d.PHI..times..times.
##EQU00008## holds, in the range of
.PHI.>.times..times.d.PHI.d.PHI.>d.PHI.d.PHI..times..times..times.
##EQU00009## holds.
A table in which these were compared is shown in Table 6. It can be
understood from this table that in a wide range
d.PHI.d.PHI.<d.PHI.d.PHI..times..times. ##EQU00010## holds.
Accordingly, large magnification can be achieved if the tilt of the
power .PHI.2 of which tilt is great in a wide range can be reduced.
Accordingly, it can be understood that upon increasing both the
principal-point interval e and the back focus Sk, the tilt can be
reduced when focusing attention on the tilt of the power .PHI.2
within Equation 20.
d.PHI.d.PHI..times..times. ##EQU00011##
Also, the distance (the entire length in thin-thickness
approximation) from the principal-point position of the first group
which is the sum of the principal-point interval e and the back
focus Sk is constant, the tilt of the power .PHI.12 at the time of
e=Sk becomes minimal. Thus, the zoom ratio becomes maximal.
With at least one exemplary embodiment, the above principal-point
interval e is substituted with the distance between the H1' and H2
as thickness increases from approximation at thin thickness, and
thin principal-point interval e is shifted. At least one exemplary
embodiment takes this point into consideration, and makes the
following arrangement.
<'<.times..times. ##EQU00012##
However, when assuming that the distance between the object point
and the H1 is e.sub.o, the distance between the H1' and H2 is e,
and the distance between the H2' and the image point is e.sub.i, e'
is a smaller distance between the e.sub.o and e.sub.i. Also, if the
back focus Sk is constant, and a principal point can be moved, the
tilts of the power .PHI.1 and .PHI.2 can be reduced to realize
large magnification by increasing the principal-point interval e.
Accordingly, employing an optical element where a principal-point
interval is increased by the shape of the surface of an optical
element making up a group as a rotational asymmetric lens enables
the principal-point interval to be increased while keeping the
surface interval as is, and further, enables large magnification to
be achieved.
If a curved surface with a single surface alone such as described
with Equation 10 as described above is employed, both forward and
backward principal-points simply move upon the same surface. Simply
employing this optical element cannot move a principal-point
position greatly. Accordingly, the zoom ratio cannot be increased
as well. If a principal-point interval can be increased by moving
this principal point forward or backward of the optical element,
large magnification can be achieved without increasing the surface
interval. Here, consideration is made regarding the principal-point
positions of three lenses of a positive lens of which both lens
surfaces have a convex shape (biconvex lens) as a coaxial lens, a
negative lens of which both lens surfaces have a concave shape
(biconcave lens), and a meniscus-shaped lens. The biconvex lens and
the biconcave lens both have a principal point within the lens, so
it cannot be expected to move a principal point outside of the lens
greatly. On the other hand, the meniscus-shaped lens, which is
different from the biconvex lens and the biconcave lens, is a lens
of which a principal point can be moved outside of the lens.
Accordingly, employing this shape even for a rotational asymmetric
lens enables a principal point to be moved outside of the lens
greatly. If this is employed for a rotational asymmetric lens such
as the zoom optical system according to at least one exemplary
embodiment, a principal-point interval can be increased to expect
large magnification.
If a principal-point interval is set small on the telephoto side,
and is set large on the wide-angle side, further large
magnification can be realized. It can be understood from Equation
6. When assuming that the power of the entire system on the
wide-angle side is .PHI..sub.w, the power of the first group and
the second group at that time are .PHI..sub.1w and .PHI..sub.2w
respectively, and the principal-point interval thereof is e.sub.w,
and similarly, the power of the entire system on the telephoto side
is .PHI..sub.t, the power of the first group and the second group
are .PHI..sub.1t and .PHI..sub.2t respectively, and the
principal-point interval thereof is e.sub.t, Equation 6 is modified
as follows.
.PHI..sub.w=.PHI..sub.1w+.PHI..sub.2w-e.sub.w.PHI..sub.1w.PHI..sub.2w
[Equation 29]
.PHI..sub.t=.PHI..sub.1t+.PHI..sub.2t-e.sub.t.PHI..sub.1t.PHI..sub.2t
(however, .PHI..sub.w>.PHI..sub.t) [Equation 30]
Here, the power .PHI..sub.1 and power .PHI..sub.2 have a different
sign, so when assuming that .PHI..sub.1w+.PHI..sub.2w>0,
.PHI..sub.1t+.PHI..sub.2t>0, and [Equation 31]
e.sub.w>e.sub.t, [Equation 32] it can be understood that the
difference between the power .PHI..sub.w and power .PHI..sub.t
becomes great, and large magnification is realized.
EXAMPLE 6
FIG. 38 is a lens cross-sectional view according to an example 6 of
at least one exemplary embodiment.
In FIG. 38, T, M, and W are lens cross-sectional views at the
telephoto end (the zoom position where the power of the entire
system is the minimum), at a middle zoom position, and at the
wide-angle end (the zoom position where the power of the entire
system is the maximum), respectively.
FIG. 39 is a lens cross-sectional view for selecting the middle
zoom position of the example 6 in FIG. 38 (M in FIG. 38) as an
example and for describing respective factors.
A zoom optical system according to the example 6 is a photography
lens system employed for an imaging apparatus, and the left hand is
the object side, and the right hand is the image side in the lens
cross-sectional view.
Note that the zoom optical system according to the example 6 can be
employed as a projector, and in this case, the left hand is a
screen, and the right hand is a projection surface.
In FIG. 38 and FIG. 39, G1h and G3h are optical groups of which
optical power is variable. G2h is an optical group in which optical
power is substantially unchangeable.
G4h is an optical group S having symmetry as to at least one
surface, and including one or more optical elements Ls capable of
moving in the optical-axis direction.
Zooming is performed while maintaining the image plane IP in a
steady manner by changing the power in the two optical groups G1h
and G3h each of which optical power is variable.
The two optical groups G1h and G3h each of which optical power is
variable each include a rotationally asymmetrical surface, move in
the direction different from the optical axis, and include two
optical elements E1h and E2h which change the power within the
optical group G1h, and two optical elements E5h and E6h which
change the power within the optical group G3h, respectively.
Note that the term "optical power" refers to the power of a surface
positioned on the optical axis, and when the surface on the optical
axis varies by the optical element having a rotationally
asymmetrical surface being decentered, optical power is also
changed in response to that change.
With the example 6 of at least one exemplary embodiment, seven
optical elements (lenses) are employed in total. In order from the
object side, the optical elements E1h, E2h, E5h, and E6h have a
rotational asymmetric shape, these optical elements are decentered
in the Y-axis direction, and the amount of decentering continuously
varies. Also, the absolute value of the amount thereof is set so as
to be equal with mutually positive/negative reverse. The optical
elements E3h and E4h have a rotational symmetric spherical surface.
In the event that an asymmetric aberration remains on the optical
axis, the optical elements E3h and E4h can have a rotational
asymmetric shape to reduce this. An optical element E7h has a
rotational asymmetric shape which has symmetry as to at least one
surface (one surface is taken as a center of symmetry). In other
words, the optical element E7h can have a rotational asymmetric
shape symmetric as to multiple surfaces (e.g., toric surfaces), but
in at least one exemplary embodiment, which is an optical element
which can have a rotational asymmetric shaped surface symmetric as
to only one surface (only one surface serving as a symmetric center
exists). The same is true of E1h, E2h, E3h, E4h, E5h, and E6h. This
is substantially similar in the following respective examples.
This reduces the on-axis coma aberration which may not have been
completely reduced in the optical elements E1h through E6h by
moving the on-axis coma aberration on the optical axis. Also, the
first group G1h comprises the optical elements E1h and E2h.
Similarly, the second group G2h comprises the optical elements E3h
and E4h, and the third group G3h comprises the optical elements E5h
and E6h. The fourth group G4h comprises the optical element E7h. As
for surface numbers, the reference plane serving as the origin of
the absolute coordinates system is determined as a surface S0, the
first surface of the optical element E1h is determined as S1h, and
in order, the corresponding surfaces are surfaces S2h, S3h, S4h,
and so on, and following the surface S6h (backward of the optical
element E3h) a diaphragm S7h (SP) is disposed.
The first surface of the optical element E4h is determined as S8h,
and the subsequent numbers are assigned in order, and the image
plane IP is S16h. Hereinafter, decentering continues in the Y-axis
direction, and let us say that the rotational asymmetric groups
(G1h and G3h), which contribute to change in power, the rotational
symmetric group (G2h), and the fourth group G4h made up of the
optical element (E7h) configured to suppress the above residual
aberration by decentering are referred to as decentering movable
blocks G1h and G3h, auxiliary block G2h, and auxiliary movable
block G4h, respectively. Disposing the decentering movable blocks
G1h and G3h alone makes the power thereof too strong, and can make
it difficult to perform correction of aberrations, and accordingly,
the auxiliary block G2h is disposed.
The lens data of the example 6 is shown in Table 7. The amount of
shift from the Z axis of the respective optical elements is shown
in Table 8.
The amount of movement in the optical-axis direction accompanied
with zooming of the optical element E7h is shown in Table 9. In
Table 9, change in intervals before and after the optical element
E7h is shown with S13h and S14h.
The values of the respective coefficients of the polynomial
surfaces represented with Equation 1 are shown in Table 10. FIG. 38
is a lens cross-sectional view at the telephoto end (T), middle
zoom position (M), and wide-angle end (W) shown in Table 8. The
optical elements E1h and E2h are decentered in the Y-axis
direction, and the absolute value of the amount thereof is so as to
be equal with mutually positive/negative reverse, as shown in Table
8. Thus, the power of the first group G1h is changed from positive
to negative between the telephoto end and the wide-angle end. The
ray emitted from the first group G1h passes through the optical
element E3h, diaphragm SP, and optical element E4h, and illuminates
the optical elements E5h and E6h. The optical elements E5h and E6h
are decentered in the Y-axis direction, and the absolute value of
the amount thereof is so as to be equal with mutually
positive/negative reverse, as shown in Table 8. Thus, the power of
the third group G3h is changed from negative to positive between
the telephoto end and the wide-angle end. The ray passed through
these decentering movable blocks G1h and G3h illuminates the next
auxiliary movable block G4h. The auxiliary movable block G4h
compensates the power necessary for the decentering movable blocks
G1h and G3h. The ray passed through these optical elements forms an
image without changing the image plane IP.
With the present example, one or more optical elements capable of
moving in the optical-axis direction at the time of zooming include
an optical element having positive refracting power.
With the present example, when assuming that the amount of movement
in the entire zoom range of one optical element (the optical
element E7h having positive refracting power in the example 6) of
one or more optical elements capable of moving in the optical-axis
direction at the time of zooming is d, and the entire length of the
entire system is T, the following condition d/T<0.6 can be
satisfied.
Thus, an aberration fluctuation caused by zooming is appropriately
corrected while restricting the entire length from being
enlarged.
The entire length (the distance between the first surface and the
image plane) T of the example 6 is 10 mm, and the movement amount d
of the optical element (auxiliary movable block) E7 is 1.34475 mm,
and consequently, d/T=1.3 is obtained.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 40A through FIG.
40C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 40A through FIG. 40C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X axis, so only the positive case should be
taken into consideration regarding the X direction. When viewing
the ray at an angle of view of 0.degree., it can be understood that
a coma aberration can be reduced from the telephoto end to the
wide-angle end.
Also, FIG. 41 illustrates the distortion reactor lattices at a
telephoto end T, middle zoom position M, and wide-angle end W. The
lengthwise and crosswise size of the lattices is about 1/4 inch
(vertically 2.7 mm.times.horizontally 3.6 mm). When viewing this
figure, it can be understood that distortion can be suppressed, but
when viewing the ray at an angle of view of 0.degree., it can be
understood that some amount of the coma aberration can remain.
FIG. 42 is a chart plotting change in power .PHI.1 and .PHI.3 of
the first group G1h and the third group G3 caused by zooming, and
the sum thereof .PHI.13(.PHI.1+.PHI.3) as to the power of the
entire system.
At this time, when assuming that the maximum value of the absolute
value of the power in the first group G1 and the third group G3h is
|.PHI.|max, and the power of the sum of the first group G1h and the
third group G3h is .PHI.13,
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max can be satisfied.
Satisfying the conditional expression (5) reduces the Petzval sum
and the image plane distortion.
FIG. 43 illustrates change in the principal-point positions before
and after the first group G1h and the third group G3h (H1 is the
forward principal-point position of the first group G1h, H1' is the
backward principal-point position of the first group G1h, H2 is the
forward principal-point position of the third group G3h, and H2' is
the backward principal-point position of the third group G3h). The
first group G1h is made up of meniscus-shaped optical elements, so
the principal-point position thereof greatly moves. Also, when
comparing the change thereof with FIG. 42, it can be understood
that the power of the first group G1h moves in the object direction
in the positive range as the power of the entire system increases,
and expands the interval of the H1 and H2.
Also, it can be understood that the power of the first group G1h
moves in the object direction even in the negative range as the
power of the entire system increases, and expands the interval of
the H1 and H2. Also, when assuming that the forward principal-point
position and the backward principal-point position of the first
group G1h are H1 and H1' respectively, the forward principal-point
position and the backward principal-point position of the third
group G3h are H2 and H2' respectively, the distance between the
object point and the H1 is eo, the distance between the H1' and H2
is e, the distance between the H2' and the image point is ei, and
smaller distance between the eo and ei is e', the relationships
between e and e' and the relationships of e/e' are shown in Table
11. When viewing this, it can be understood that the e and e' are
essentially the same at any zoom position.
Particularly, 0.7<e/e'<1.4 can be satisfied.
Further, as illustrated in FIG. 43, when assuming that the backward
principal-point position of the first group G1h is H1', the forward
principal-point position of the third group G3h is H2, the distance
between the H1' and H2 in a case in which the power of the entire
system is the smallest in the positive range of the power of the
first group G1h at zooming (telephoto end) is et1, the distance
between the H1' and H2 in a case in which the power of the entire
system is the greatest (wide-angle end) is ew1, the distance
between the H1' and H2 in a case in which the power of the entire
system is the smallest in the negative range of the power of the
first group G1h at zooming is et2, and the distance between the H1'
and H2 in a case in which the power of the entire system is the
greatest is ew2, it can be understood from FIG. 43 that et1<ew1,
et2<ew2 can be satisfied.
Also, with the present example, when assuming that within the
entire zoom range, the maximum value of the values obtained by
dividing the maximum value of the absolute value of each
image-forming magnification of the multiple optical elements E1h,
E2h, E5h, and E6h of the multiple optical groups G1h and G3h of
which optical power is variable by the minimum value is Bd max, and
the maximum value of the values obtained by dividing the minimum
value of the absolute value of each image-forming magnification of
the one or more optical elements (the optical element E7h alone in
the present example) E7h capable of moving in the optical-axis
direction by the minimum value is Bs min, the following condition
Bs min<Bd max can be satisfied.
Also, when assuming that the amount of change in the optical-axis
direction caused by zooming from the telephoto end to the
wide-angle end of the forward principal-point position H.sub.A of
the optical group G1h of the multiple optical groups G1h and G3h of
which optical power is variable is .DELTA.H.sub.A, the amount of
change in the optical-axis direction caused by zooming from the
telephoto end to the wide-angle end of the forward principal-point
position H.sub.B of the optical group G3h closer to the image side
than the optical group G1h is .DELTA.H.sub.B, greater amount of
change between the amount of change .DELTA.H.sub.A and the amount
of change .DELTA.H.sub.B is .DELTA.H.sub.d max, and the amount of
change of the forward principal-point position of the one or more
optical elements E7h is .DELTA.H.sub.S, the following condition
.DELTA.H.sub.S<.DELTA.H.sub.d max can be satisfied.
Specifically, as illustrated in FIG. 43, the .DELTA.H.sub.d max is
2.025 from change in the principal-point interval of the first
group G1h, and .DELTA.H.sub.S is 1.489 by calculating the amount of
movement of the S13 from Table 9. That is to say, it can be
understood that .DELTA.H.sub.d max<.DELTA.H.sub.S is
satisfied.
Next, Table 12 shows change in image-forming magnification at the
telephoto end, middle, and wide-angle end for each of the optical
elements E1h, E2h, E5h, E6h, and E7h.
The optical elements E1h, E2h, E5h, and E6h are optical elements Ld
which are decentering movable, and the optical element E7h is an
optical element Ls which moves in the optical-axis direction. The
maximum value Bd max is 263.97 at the optical element E5h, and on
the other hand, the minimum value Bs min is 1.0193 at the optical
element E7h. That is to say, it can be understood that Bd max>Bs
min holds.
Note that with the present example and the following examples,
focusing can be performed by moving the entire system, or by moving
one optical group in the vertical direction as to the optical
axis.
EXAMPLE 7
FIG. 44 is a lens cross-sectional view at the telephoto end (T),
middle zoom position (M), and wide-angle end (W) according to the
example 7 of at least one exemplary embodiment.
FIG. 45 is a lens cross-sectional view for selecting the middle
zoom position of the example 7 in FIG. 44 as an example and for
describing respective factors.
With the example 7, six optical elements are employed in total. In
order from the object side (forward) to the image side, optical
elements E1i, E2i, E3i, and E4i have a rotational asymmetric shape,
these optical elements are decentered in the Y-axis direction, and
the amount of decentering continuously varies.
Also, the absolute value of the amount thereof is set so as to be
equal with mutually positive/negative reverse. The optical elements
E5i and E6i have a rotational symmetric aspheric surface. In the
event that an asymmetric aberration remains on the optical axis,
the optical elements E5i and E6i can have a rotational asymmetric
shape to reduce this.
The optical elements E5i and E6i perform aid of movement power
integrally in the optical-axis direction at the time of zooming.
Also, a first group G1i comprises the optical elements E1i and E2i,
and similarly, a second group G2i comprises the optical elements
E3i and E4i.
As for surface numbers, the reference plane serving as the origin
of the absolute coordinates system is determined as a surface S0,
the first surface of the optical element E1i is determined as S1i,
and in order, the corresponding surfaces are surfaces S2i, S3i, and
S4i, and following the surface S4i (backward of the optical element
E2i) a diaphragm S5i (SP) is disposed. The first surface of the
optical element E3i is determined as S6i, and the subsequent
numbers are assigned in order, and the image plane is S17i.
Hereinafter, let us say that the rotational asymmetric groups
(optical elements E1i through E4i), which are continuously
decentered in the Y-axis direction, and the rotational symmetric
groups (optical elements E5i and E6i) are referred to as
decentering movable blocks G1i and G2i, and an auxiliary movable
block G3i.
Disposing the decentering movable blocks G1i and G2i alone makes
the power thereof too strong, and can make it difficult to perform
correction of an aberration, and accordingly, the auxiliary movable
block is disposed. Also, both surfaces of the optical elements E1i
through E4i having a rotational asymmetric shape have a
rotationally asymmetrical surface shape. A flat-plate glass block
Ga disposed immediately prior to a CCD surface, a CMOS surface, or
other related or equivalent image pickup apparatus as known by one
of ordinary skill in the relevant art is an infrared cut filter and
the cover glass of a CCD (e.g., or CMOS).
The lens data of the example 7 is shown in Table 13. The amount of
shift from the Z axis of each of the optical elements E1i through
E4i is shown in Table 14, and the amount of movement in the
optical-axis direction of the optical elements E5i and E6i shown in
the surface S9i and surface S13i is shown in Table 15. Further, the
coefficients of the rotational symmetric aspheric shapes
represented with the following equation are shown in Table 16, and
the coefficients represented with Equation 33 are shown in Table
17.
.times..times..times..times..times. ##EQU00013##
Here, Z is the displacement in the optical-axis direction at a
position of a height h from the optical axis on the basis of a
surface peak.
However, with the above equation, h2=X2+Y2 can be satisfied, c is a
curvature radius, and A and B are coefficients.
It can be understood that the entire length is 6.9 mm, so when
calculating a ratio between this and 0.06062 mm, 0.00879 is
obtained, and this is included in the range of Equation 23.
In FIG. 44, the ray illuminated a reference plane S0 first
illuminates the first group G1i. The first group G1i is made up of
the two optical elements E1i and E2i, and the surface numbers are
S1i through S4i. The optical elements E1i and E2i are decentered in
the Y-axis direction, and the absolute value of the amount thereof
is so as to be equal with mutually positive/negative reverse, as
shown in Table 4. Thus, the power of the first group G1i is changed
from positive to negative at the time of zooming from the telephoto
end to the wide-angle end.
The ray emitted from the first group G1i next passes through the
diaphragm S5i, and illuminates the second group G2i. The second
group G2i, as with the first group G1i, comprises two optical
elements E3i and E4i, and the surface numbers thereof are S6i
through S9i. The optical elements E3i and E4i are decentered in the
Y-axis direction, and the absolute value of the amount thereof is
so as to be equal with mutually positive/negative reverse, as shown
in Table 4.
Thus, the power of the second group G2i is changed from negative to
positive at the time of zooming from the telephoto end to the
wide-angle end. The ray passed through these decentering movable
blocks G1i and G2i illuminates the next auxiliary movable block
G3i. The auxiliary movable block G3i compensates the power
necessary for the decentering movable blocks G1i and G2i. The
auxiliary movable block G3i comprises the optical elements E5i and
E6i made up of surfaces S10i through S13i which are rotational
symmetric aspheric surfaces. The ray passed through these optical
elements passes through an infrared cut filter and the cover glass
of a CCD (e.g., or CMOS), and forms an image without changing the
image plane.
Next, the aberration charts at the telephoto end, middle zoom
position, and wide-angle end are shown in FIG. 46A through FIG.
46C, respectively. The horizontal axis represents the position of a
ray on the pupil, and the vertical axis represents the shift from
the chief ray on the image plane. The range of the vertical axis is
about .+-.20 .mu.m. The numbers within FIG. 46A through FIG. 46C
are angle-of-view numbers, which on the image plane are such as
illustrated in FIG. 8. The shapes of the optical elements are
symmetric as to the X axis, so only the case of the positive X
direction should be taken into consideration.
When viewing the ray at an angle of view of 0.degree., it can be
understood that a coma aberration can be reduced from the telephoto
end to the wide-angle end. Also, FIG. 47 illustrates distortion
lattices. The lengthwise and crosswise size of the lattices is
about 1/4 inch (vertically 2.7 mm.times.horizontally 3.6 mm). When
viewing this, it can be understood that distortion is appropriately
suppressed.
FIG. 48 is a chart plotting change in power .PHI.1 and .PHI.2 of
the first group G1i and second group G2i, and the sum thereof
.PHI.1+.PHI.2 as to the power of the entire system.
When assuming that the maximum value of the absolute value of the
power in the first group G1i and second group G2i is |.PHI.|max,
the total value of the power in the first group G1i and second
group G2i at an arbitrary zoom position is .PHI.2, a greater value
between the absolute value of the power of the first group G1i and
the absolute value of the power of the second group G2i at the
wide-angle end is |.PHI.gw|max, and a smaller value between the
absolute value of the power of the first group G1i and the absolute
value of the power of the second group G2i at the telephoto end is
|.PHI.gt|min, |.PHI.gw|max<|.PHI.gt|min can be satisfied.
Also, -|.PHI.|max.ltoreq..PHI.12.ltoreq.|.PHI.|max can be
satisfied.
Also, the intersection of change in power .PHI.1 and .PHI.2 of the
first group G1i and second group G2i is disposed closer to the side
having great optical power (wide-angle end) than the zoom middle
position. Thus, zooming is effectively performed.
Next, Table 18 shows change in the image-forming magnification of
each of the optical elements E1i through E6 at the telephoto end,
middle, and wide-angle end. The optical elements E1i, E2i, E3i, and
E4i are optical elements Ld which are decentering movable, and the
optical elements E5i and E6i are optical elements Ls which move in
the optical-axis direction. The maximum value Bd max is 10.384 at
the optical element E3i, and on the other hand, the minimum value
Bs min is 1.00056 at the optical element E6i. That is to say, it
can be understood that Bd max>Bs min holds.
As described above, according to each of the examples, zooming is
performed employing a block including an optical element which
moves in the optical-axis direction as well as the decentering
movable blocks, thereby performing zooming while appropriately
eliminating an aberration, and also obtaining a compact zoom
optical system.
Note that with the above respective examples, three or more optical
groups of which optical power is variable can be employed. Also,
two or more optical groups having symmetry as to at least one
surface, and including one or more optical elements capable of
moving in the optical-axis direction can be employed. Also, an
optical group of which optical power is substantially unchangeable
can be omitted, or two or more optical groups of which optical
power is substantially unchangeable can be employed.
The above examples 6 and 7 achieve a zoom optical system capable of
sufficiently eliminating an aberration even at the time of zooming
by adding an optical element capable of moving in the optical-axis
direction to solve the problems (a) and (b) in the above
comparative example 1.
Also, with the examples 6 and 7, correction of power can be
performed by disposing a coaxial lens (coaxial optical element)
within an optical path to suppress the power of the decentering
movable block, thereby suppressing an on-axis coma aberration.
Also, comparison will be made between the examples 6 and 7 and the
comparative example 2. With the above equations, it is a condition
for large magnification that the e and e' are essentially equal.
Further, when assuming that the entire length is 1, it can be
understood that the e or e' is greater than 0.4167 but less than
0.588 from e+e'=1 0.7<e/e'<1.4 [Equation 34]
If we consider inserting an auxiliary movable block therebetween
such as in at least one exemplary embodiment, it can be understood
that the maximum value of the amount of movement in the
optical-axis direction of the auxiliary movable block can be less
than 0.588. Further, at least one exemplary embodiment takes the
shift of a principal point into consideration, and sets the amount
of movement of the auxiliary movable block to the following range.
d/T<0.6 [Equation 35]
Further, setting the auxiliary movable block to positive power
enables the power of the decentering movable block to be
loosed.
Also, the auxiliary movable block is provided for correction of the
decentering movable block, so is a block of which change in
magnification is loosed as compared with the decentering movable
block. That is to say, satisfying the following range enables the
power of the decentering movable block to be loosed, and
consequently, an aberration is reduced as a whole. Bd max>Bs min
[Equation 36]
Also, for the same reason as the above, it can be necessary in some
circumstances to compare change in the principal-point position of
the decentering movable block with that of the auxiliary movable
block, and enlarge the former. Accordingly, an aberration is
suppressed by satisfying the following range. .DELTA.Hd
max>.DELTA.Hs [Equation 37]
As described above, an asymmetric aberration such as a on-axis coma
aberration is suppressed by moving the auxiliary movable block.
Also, the power of the decentering movable block can be set as
follows.
When assuming that a greater absolute value between the absolute
value of the power of the first group G1 and that of the third
group G3 at the wide-angle end is |.PHI.gw|max, a smaller absolute
value between the power of the respective groups at the telephoto
end is |.PHI.gt|min, the power at the wide-angle end is earned by
satisfying Equation 38. |.PHI.gw|max<|.PHI.gt|min [Equation
38]
Further, it has been known that if the Petzval is great, the
curvature of field also becomes great, and if the Petzval is small,
the curvature of field also becomes small.
Accordingly, at least one exemplary embodiment suppresses the
curvature of field to small by reducing the Petzval. When the power
at lenses Ei (i=1 through n) is .PHI.Ei, and the refractive index
of a material is nEi, the Petzval is obtained with the following
equation. PEi=.PHI.Ei/nEi [Equation 39]
With a normal zoom optical system using a coaxial optical element,
this value can be constant. However, this value is not constant
with an optical system such as in at least one exemplary embodiment
where an optical element is continuously decentered, and power
varies. Also, the refractive index of a nitrifying material is
around 1.45 through 1.9, so change thereof is small, and
accordingly, change in the Petzval can be referred to change in
power.
Accordingly, in order to suppress this Petzval, when assuming that
the maximum value of the absolute value of the power in the A group
and the B group is |.PHI.|max, and the power in total of the A
group and the third group G3a-i is .PHI.13, the range of change in
power is determined so as to satisfy the following equation.
-|.PHI.|max.ltoreq..PHI.13.ltoreq.|.PHI.|max [Equation 40]
Next, description will be made from the perspective of a
principal-point position.
In order to perform zooming while maintaining compactness, it can
be necessary in some circumstances to move a principal-point
position greatly from a certain position of each group. With the
conventional optical system in which a tertiary curve is simply
given to a single surface, a principal-point position exists only
upon the surface with the tertiary coefficient thereof, and does
not fluctuate greatly.
As for a method for fluctuating a principal-point position greatly,
for example, an arrangement can be made where curvature is given to
a single surface, and the shape of a rotational asymmetric lens is
changed into a meniscus shape. The lens which can have a meniscus
shape, which is different from a positive lens and a negative lens,
is a lens capable of disposing a principal point outside of the
lens, and employing this shape for the rotational asymmetric lens
enables a principal point to be greatly fluctuated outside of the
group. However, when making the rotational asymmetric lens into a
meniscus shape, shifting occurs upon the upper line and underline
of the marginal ray at the telephoto end or the wide-angle end
(when the ray passes through the end of the lens). Accordingly, it
is useful for another lens to correct this.
With a method for solving this, the lens for correction is changed
into a meniscus shape, which can have a reverse tilt to cancel out
the shift of the upper line and underline. A coefficient is
determined by focusing attention on this at the time of introducing
a higher order coefficient than a tertiary coefficient. Also, a
meniscus shape can be shaped in the direction for reducing the
mutual distance. This is because reducing the distance between the
lenses enables a on-axis coma aberration to be reduced while
suppressing this to the minimum upon each surface.
As described above, the present examples 6 and 7 reduce a on-axis
coma aberration.
TABLE-US-00001 TABLE 1 a: 4.0000E-03 n: 1.51742 Amount of .delta.
deviation E1 E2 E3 E4 Telephoto end 3.00 mm -3.00 mm -1.18 mm 1.18
mm Middle 0.29 mm -0.29 mm 2.18 mm -2.18 mm Wide-angle end -1.65 mm
1.65 mm 3.89 mm -3.89 mm
TABLE-US-00002 TABLE 2 Type of surface Surface interval Object
surface Infinity S0 Reference 0 plane S1 Flat surface 1 S2
Polynomial surface 0.5 S3 Polynomial surface 1 S4 Flat surface 0.4
S5 Diaphragm 0.4 surface S6 Flat surface 1 S7 Polynomial surface
0.5 S8 Polynomial surface 1 S9 Flat surface
TABLE-US-00003 TABLE 3 Type of surface Curvature radius Surface
interval Refractive index Abbe number Object surface Reference
plane s0 0 s1 Polynomial surface 0.5 1.538604 65.5527 s2 Polynomial
surface 0.3 s3 Polynomial surface 0.5 1.589647 62.0231 s4
Polynomial surface 0.1 s6 Spherical surface 0.712795 0.5 1.48749
70.4058 s7 Spherical surface 0.853974 0.929661 Diaphragm surface
0.251098 s8 s9 Spherical surface 0.452264 0.5 1.48749 70.4058 s10
Spherical surface 0.246629 0.819241 s11 Polynomial surface 0.6
1.62041 60.3236 s12 Polynomial surface 0.5 s13 Polynomial surface
0.6 1.62041 60.3236 s14 Polynomial surface 0.2 s15 Spherical
surface 0.19521 0.7 1.48749 70.4058 s16 Spherical surface 0.05331 3
Image plane
TABLE-US-00004 TABLE 4 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.89952 0.49385 -0.60408 E2 -0.89952
-0.49385 0.60408 E5 -1.22297 -0.29356 0.58002 E6 1.22297 0.29356
-0.58002
TABLE-US-00005 TABLE 5 S1 C2: 7.25E-02 C3: -2.17E-02 C4: -6.26E-03
C5: 1.22E-03 C6: 5.61E-04 C20: 1.44E-01 C21: -4.85E-02 C22:
-1.05E-02 C23: -1.59E-03 C24: 1.95E-03 C40: 2.90E-04 C41: 1.37E-03
C42: 2.20E-03 C60: -4.96E-04 S2 C2: 8.88E-02 C3: 4.58E-04 C4:
-6.74E-03 C5: 1.68E-03 C6: 6.93E-04 C20: 1.41E-01 C21: 1.98E-02
C22: -1.06E-02 C23: -1.32E-03 C24: 1.47E-03 C40: 1.08E-02 C41:
6.24E-03 C42: 2.97E-03 C60: -7.26E-04 S3 C2: 4.49E-02 C3: 5.69E-03
C4: 6.07E-03 C5: 2.35E-04 C6: -4.21E-05 C20: 1.02E-01 C21:
-2.38E-02 C22: 4.02E-02 C23: 2.44E-03 C24: -4.75E-03 C40: 2.87E-02
C41: -3.42E-03 C42: -7.96E-03 C60: -1.15E-03 S4 C2: 6.12E-02 C3:
-2.26E-02 C4: 1.06E-02 C5: -1.41E-03 C6: 5.87E-05 C20: 1.71E-01
C21: -1.38E-01 C22: 7.36E-02 C23: -1.47E-02 C24: -2.46E-03 C40:
3.38E-02 C41: -2.19E-02 C42: -4.05E-03 C60: -1.28E-03 S11 C2:
-2.00E-02 C3: 2.91E-02 C4: 6.76E-03 C5: -2.34E-03 C6: -2.23E-03
C20: 1.19E-02 C21: 8.79E-02 C22: 6.91E-03 C23: -1.83E-02 C24:
-1.06E-02 C40: 2.13E-02 C41: -2.43E-02 C42: -2.76E-02 C60:
-6.62E-03 S12 C2: -4.15E-02 C3: 7.74E-02 C4: 8.72E-03 C5: -1.55E-03
C6: -2.17E-03 C20: -1.00E-01 C21: 1.58E-01 C22: 2.16E-02 C23:
-1.26E-02 C24: -9.10E-03 C40: 6.61E-03 C41: -2.38E-02 C42:
-1.94E-02 C60: -1.42E-03 S13 C2: -5.49E-03 C3: 3.23E-02 C4:
-1.21E-02 C5: -1.63E-03 C6: 9.65E-04 C20: -1.61E-01 C21: 8.58E-02
C22: 1.15E-03 C23: -3.03E-03 C24: -1.78E-04 C40: -2.17E-04 C41:
2.42E-03 C42: -2.40E-03 C60: -2.36E-03 S14 C2: -2.64E-02 C3:
-1.02E-02 C4: -7.90E-03 C5: -2.20E-03 C6: 7.70E-04 C20: -1.11E-01
C21: -4.63E-02 C22: 1.04E-02 C23: -3.82E-03 C24: -1.01E-04 C40:
1.27E-02 C41: -2.64E-03 C42: 4.33E-04 C60: -9.88E-05
TABLE-US-00006 TABLE 6 .phi. . . . ##EQU00014## . . . ##EQU00015##
. . . d.PHI.d.PHI. ##EQU00016## Small Small Small Equal Great
d.PHI.d.PHI. ##EQU00017## Great Great Great Equal Small
TABLE-US-00007 TABLE 7 Type of surface Surface interval Refractive
index Abbe number Object surface Infinity Reference plane s0 Flat
surface 0 s1 Polynomial surface 0.5 1.48749 70.4 s2 Polynomial
surface 0.3 s3 Polynomial surface 0.5 1.48749 70.4 s4 Polynomial
surface 0.1 s5 Spherical surface 0.5 1.48749 70.4 s6 Spherical
surface 0.929645 Diaphragm surface Flat surface 0.251071 s7 s8
Spherical surface 0.5 1.48749 70.4 s9 Spherical surface 0.819284
s10 Polynomial surface 0.6 1.5759 62.9 s11 Polynomial surface 0.5
s12 Polynomial surface 0.6 1.518951 67.2 s13 Polynomial surface 0.2
s14 Polynomial surface 0.7 1.48749 70.4 s15 Polynomial surface 3
Image plane Flat surface
TABLE-US-00008 TABLE 8 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.9722 0.53763 -0.51577 E2 -0.9722
-0.53763 0.51577 E5 -1.25554 -0.39583 0.50539 E6 1.25554 0.39583
-0.50539 E7 -0.68683 -0.09902 0.13684
TABLE-US-00009 TABLE 9 S1 C2 4.78E-02 C3 -2.66E-02 C4 -6.58E-03 C5
9.93E-04 C6 5.80E-04 C20 1.15E-01 C21 -2.81E-02 C22 -1.31E-03 C23
8.59E-04 C24 1.43E-03 C40 -3.96E-04 C41 2.11E-03 C42 2.44E-04 C60
-3.19E-04 S2 C2 7.97E-02 C3 -1.73E-03 C4 -6.48E-03 C5 1.28E-03 C6
5.89E-04 C20 1.41E-01 C21 4.90E-02 C22 4.78E-03 C23 4.28E-03 C24
1.60E-03 C40 1.42E-02 C41 9.64E-03 C42 1.92E-03 C60 -2.41E-03 S3 C2
3.70E-02 C3 2.38E-02 C4 -2.77E-03 C5 -9.88E-04 C6 6.87E-04 C20
8.86E-02 C21 1.13E-02 C22 1.74E-02 C23 -9.86E-04 C24 -7.13E-04 C40
2.02E-02 C41 2.41E-03 C42 -3.74E-03 C60 -4.76E-03 S4 C2 7.25E-02 C3
-9.45E-03 C4 8.74E-04 C5 -2.60E-03 C6 9.37E-04 C20 1.65E-01 C21
-1.04E-01 C22 4.03E-02 C23 -1.37E-02 C24 1.45E-03 C40 1.80E-02 C41
-7.75E-03 C42 -2.20E-03 C60 -3.26E-03 S10 C2 -2.61E-02 C3 3.20E-02
C4 7.15E-03 C5 6.86E-04 C6 -2.70E-03 C20 1.24E-02 C21 -1.37E-02 C22
1.49E-02 C23 -7.80E-03 C24 -1.13E-02 C40 -4.54E-03 C41 8.90E-03 C42
-1.89E-02 C60 -7.19E-04 S11 C2 -3.79E-02 C3 8.01E-02 C4 1.19E-02 C5
2.87E-03 C6 -1.77E-03 C20 1.62E-02 C21 8.61E-02 C22 2.45E-02 C23
-1.27E-03 C24 -8.91E-03 C40 -3.90E-02 C41 1.95E-02 C42 -8.91E-03
C60 4.55E-03 S12 C2 -1.74E-02 C3 3.03E-02 C4 -1.01E-02 C5 -9.73E-04
C6 5.68E-04 C20 6.62E-02 C21 8.09E-03 C22 -8.75E-03 C23 4.91E-03
C24 -9.23E-04 C40 -1.73E-02 C41 1.43E-02 C42 -6.34E-03 C60
-2.61E-03 S13 C2 -3.94E-02 C3 -1.80E-02 C4 -6.10E-03 C5 -1.82E-03
C6 5.02E-04 C20 2.07E-02 C21 -1.54E-01 C22 2.16E-03 C23 2.85E-03
C24 3.73E-04 C40 3.29E-03 C41 6.87E-03 C42 -1.49E-03 C60 3.77E-03
S14 C2 1.12E-01 C3 9.54E-03 C4 -1.83E-02 C5 -7.46E-04 C6 -4.60E-03
C20 2.61E-01 C21 -8.66E-02 C22 -2.18E-02 C23 -6.73E-03 C24 4.42E-03
C40 -4.66E-02 C41 1.69E-02 C42 1.60E-02 C60 2.59E-03 S15 C2
6.96E-02 C3 9.14E-03 C4 -2.20E-02 C5 -1.33E-03 C6 -5.00E-03 C20
2.43E-01 C21 -1.16E-02 C22 -2.15E-02 C23 -1.64E-02 C24 2.79E-03 C40
-4.71E-02 C41 1.02E-02 C42 1.42E-02 C60 -9.36E-05
TABLE-US-00010 TABLE 10 e e' e/e' 1 4.66486 4.40074 1.060017 2
4.77492 4.43732 1.076082 3 4.99275 4.47979 1.114505 4 5.891 4.61327
1.276968 5 3.5578 3.80655 0.934652 6 4.21107 4.29634 0.980153
TABLE-US-00011 TABLE 11 Type of surface Surface interval Refractive
index Abbe number Object surface Infinity Reference plane Flat
surface 0 s0 s1 Polynomial surface 0.5 1.48749 70.4 s2 Polynomial
surface 0.3 s3 Polynomial surface 0.5 1.48749 70.4 s4 Polynomial
surface 0.1 s5 Spherical surface 0.5 1.48749 70.4 s6 Spherical
surface 0.929645 Diaphragm Flat surface 0.251071 surface s7 s8
Spherical surface 0.5 1.48749 70.4 s9 Spherical surface 0.819284
s10 Polynomial surface 0.6 1.549101 64.7 s11 Polynomial surface 0.5
s12 Polynomial surface 0.6 1.582253 67.2 s13 Polynomial surface
1.43067 s14 Polynomial surface 0.7 1.744251 44.2 s15 Polynomial
surface 1.76933 Image plane Flat surface
TABLE-US-00012 TABLE 12 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.90459 0.51376 -0.56819 E2 -0.90459
-0.51376 0.56819 E5 -1.25999 -0.31844 0.59454 E6 1.25999 0.31844
-0.59454
TABLE-US-00013 TABLE 13 Amount of tilt Lens number Telephoto end
Middle Wide-angle end E7 -0.68683 -0.09902 0.13684
TABLE-US-00014 TABLE 14 S1 C2 6.50E-02 C3 -2.42E-02 C4 -6.49E-03 C5
8.62E-04 C6 6.90E-04 C20 1.22E-01 C21 -3.62E-02 C22 -2.16E-03 C23
-4.12E-04 C24 1.58E-03 C40 4.36E-03 C41 1.12E-03 C42 3.67E-04 C60
-5.42E-04 S2 C2 8.79E-02 C3 1.17E-03 C4 -6.78E-03 C5 1.03E-03 C6
6.84E-04 C20 1.34E-01 C21 4.33E-02 C22 4.58E-04 C23 9.45E-04 C24
9.73E-04 C40 1.37E-02 C41 6.02E-03 C42 8.06E-04 C60 -2.68E-03 S3 C2
3.48E-02 C3 1.04E-02 C4 5.84E-03 C5 -4.63E-04 C6 -1.20E-04 C20
8.33E-02 C21 7.76E-03 C22 2.98E-02 C23 3.16E-03 C24 -3.16E-03 C40
2.02E-02 C41 1.08E-04 C42 -6.92E-03 C60 -4.05E-03 S4 C2 6.14E-02 C3
-2.31E-02 C4 1.05E-02 C5 -2.32E-03 C6 3.23E-05 C20 1.59E-01 C21
-1.15E-01 C22 5.30E-02 C23 -7.61E-03 C24 -1.91E-03 C40 2.33E-02 C41
-1.09E-02 C42 -6.00E-03 C60 -2.54E-03 S10 C2 -2.08E-02 C3 3.15E-02
C4 5.00E-03 C5 -2.72E-04 C6 -2.39E-03 C20 2.75E-02 C21 4.81E-03 C22
9.22E-03 C23 -5.95E-03 C24 -1.33E-02 C40 2.36E-02 C41 1.18E-04 C42
-2.04E-02 C60 -6.02E-03 S11 C2 -3.50E-02 C3 8.07E-02 C4 9.08E-03 C5
1.28E-03 C6 -2.44E-03 C20 -2.99E-02 C21 1.48E-01 C22 2.60E-02 C23
-6.29E-04 C24 -1.33E-02 C40 1.14E-02 C41 2.89E-03 C42 -1.46E-02 C60
-3.61E-03 S12 C2 -2.10E-02 C3 2.70E-02 C4 -1.09E-02 C5 -2.30E-03 C6
3.99E-04 C20 -5.77E-02 C21 6.67E-03 C22 2.16E-02 C23 6.06E-03 C24
-2.39E-03 C40 7.33E-03 C41 9.82E-03 C42 -1.07E-02 C60 -2.46E-03 S13
C2 -2.89E-02 C3 -2.22E-02 C4 -8.53E-03 C5 -2.74E-03 C6 3.05E-04 C20
-9.03E-02 C21 -1.40E-01 C22 3.33E-02 C23 5.08E-03 C24 -1.55E-03 C40
2.18E-02 C41 1.39E-03 C42 -5.96E-03 C60 3.64E-03 S14 C2 2.48E-01 C3
-4.50E-02 C4 -7.67E-03 C5 4.22E-03 C6 -6.63E-03 C20 1.03E-01 C21
-9.87E-02 C22 -2.17E-02 C23 9.05E-03 C24 2.51E-03 C40 -2.17E-03 C41
1.23E-02 C42 5.53E-03 C60 -2.54E-03 S15 C2 2.73E-01 C3 -6.77E-02 C4
-1.10E-02 C5 1.46E-02 C6 -1.37E-02 C20 1.23E-01 C21 -1.00E-01 C22
-1.76E-02 C23 8.90E-03 C24 2.15E-04 C40 -3.09E-03 C41 1.44E-02 C42
2.72E-03 C60 -4.45E-03
TABLE-US-00015 TABLE 15 e e' e/e' 1 4.6555 4.36899 1.065578 2
4.74743 4.39491 1.080211 3 4.89929 4.42095 1.108198 4 5.30788
4.51597 1.175358 5 1.68025 4.07459 0.412373 6 4.08146 4.30733
0.947561
TABLE-US-00016 TABLE 16 Type of surface Curvature radius Surface
interval Refractive index Abbe number Object surface Infinity
Reference plane s0 Flat surface 0 s1 Polynomial surface 0.5
1.538604 65.6 s2 Polynomial surface 0.3 s3 Polynomial surface 0.5
1.589647 62.06 s4 Polynomial surface 0.1 s5 Spherical surface
1.513485 0.5 1.48749 70.46 s6 Spherical surface 1.281722 0.896555
Diaphragm surface Flat surface 0.166764 s7 s8 Spherical surface
2.336814 0.5 1.48749 70.46 s9 Spherical surface 5.596556 0.936681
s10 Polynomial surface 0.6 1.62041 60.36 s11 Polynomial surface 0.5
s12 Polynomial surface 0.6 1.62041 60.36 s13 Polynomial surface 0.2
s14 Spherical surface 3.728692 0.7 1.48749 70.46 s15 Spherical
surface 6.173476 3 Image plane Flat surface
TABLE-US-00017 TABLE 17 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.90725 0.50479 -0.56622 E2 -0.90725
-0.50479 0.56622 E5 -1.23808 -0.32928 0.55396 E6 1.23808 0.32928
-0.55396
TABLE-US-00018 TABLE 18 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E7 -0.18878 0.01009 0.00099
TABLE-US-00019 TABLE 19 S1 C2 6.57E-02 C3 -2.26E-02 C4 -7.34E-03 C5
7.69E-04 C6 6.69E-04 C20 1.42E-01 C21 -4.40E-02 C22 -6.74E-03 C23
-3.97E-04 C24 1.85E-03 C40 9.76E-04 C41 9.37E-04 C42 1.77E-03 C60
-8.97E-04 S2 C2 8.88E-02 C3 -7.93E-05 C4 -8.01E-03 C5 9.31E-04 C6
7.17E-04 C20 1.29E-01 C21 2.33E-02 C22 -4.38E-03 C23 1.43E-03 C24
1.54E-03 C40 1.27E-02 C41 6.95E-03 C42 2.84E-03 C60 -9.50E-04 S3 C2
3.94E-02 C3 5.74E-03 C4 3.40E-03 C5 -1.89E-04 C6 -9.92E-05 C20
8.19E-02 C21 -1.09E-02 C22 3.71E-02 C23 1.98E-04 C24 -4.10E-03 C40
2.00E-02 C41 -1.28E-03 C42 -5.83E-03 C60 -1.14E-03 S4 C2 6.29E-02
C3 -2.27E-02 C4 7.39E-03 C5 -2.15E-03 C6 1.97E-04 C20 1.68E-01 C21
-1.18E-01 C22 6.86E-02 C23 -1.63E-02 C24 -1.60E-03 C40 1.83E-02 C41
-1.26E-02 C42 -4.47E-03 C60 -1.57E-03 S10 C2 -1.77E-02 C3 2.80E-02
C4 7.40E-03 C5 -1.08E-03 C6 -2.12E-03 C20 2.08E-02 C21 3.33E-02 C22
1.28E-02 C23 -1.51E-02 C24 -1.09E-02 C40 1.74E-02 C41 -2.60E-02 C42
-3.01E-02 C60 -7.57E-03 S11 C2 -4.30E-02 C3 7.36E-02 C4 1.16E-02 C5
3.34E-04 C6 -2.18E-03 C20 -8.35E-02 C21 1.75E-01 C22 3.14E-02 C23
-1.00E-02 C24 -1.15E-02 C40 1.85E-02 C41 -2.37E-02 C42 -2.60E-02
C60 -6.31E-03 S12 C2 -1.20E-02 C3 3.04E-02 C4 -7.73E-03 C5
-1.46E-03 C6 7.05E-04 C20 -1.57E-01 C21 9.49E-02 C22 -1.03E-02 C23
-9.48E-03 C24 2.28E-03 C40 1.40E-02 C41 -6.51E-03 C42 2.67E-03 C60
-3.79E-03 S13 C2 -3.31E-02 C3 -9.97E-03 C4 -5.24E-03 C5 -1.89E-03
C6 7.18E-04 C20 -1.14E-01 C21 -3.38E-02 C22 8.50E-04 C23 -9.86E-03
C24 1.67E-03 C40 1.43E-02 C41 -7.61E-03 C42 3.01E-03 C60
-4.04E-04
TABLE-US-00020 TABLE 20 e e' e/e' 1 4.58012 4.40445 1.039885 2
4.67492 4.4328 1.05462 3 4.84519 4.46744 1.084556 4 5.31689 4.64737
1.144064 5 2.1566 4.21798 0.511287 6 3.93389 4.3934 0.895409
TABLE-US-00021 TABLE 21 Type of surface Curvature radius Surface
interval Refractive index Abbe number Object surface Infinity
Reference plane s0 Flat surface 0 s1 Polynomial surface 0.5 1.48749
70.4 s2 Polynomial surface 0.3 s3 Polynomial surface 0.5 1.48749
70.4 s4 Polynomial surface 0.1 s5 Spherical surface 1.778863 0.5
1.48749 70.4 s6 Spherical surface 1.549574 0.929645 Diaphragm
surface Flat surface 0.251071 s7 s8 Spherical surface 2.574972 0.5
1.48749 70.4 s9 Spherical surface 37.2687 0.819284 s10 Polynomial
surface 0.6 1.556781 64.8 s11 Polynomial surface 0.5 s12 Polynomial
surface 0.6 1.62041 60.3 s13 Polynomial surface 0.50847 s14
Polynomial surface 0.7 1.755201 27.6 s15 Polynomial surface
0.222088 s16 Polynomial surface 0.7 1.755201 27.6 s17 Polynomial
surface 1.76944 Image plane Flat surface
TABLE-US-00022 TABLE 22 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.9074 0.51109 -0.56432 E2 -0.9074
-0.51109 0.56432 E5 -1.2605 -0.32101 0.59761 E6 1.2605 0.32101
-0.59761
TABLE-US-00023 TABLE 23 Amount of tilt Lens number Telephoto end
Middle Wide-angle end E7 -4.35122 -0.2827 1.43592 E8 -2.42017
-0.76772 -1.46017
TABLE-US-00024 TABLE 24 S1 C2 5.97E-02 C3 -2.31E-02 C4 -5.57E-03 C5
1.01E-03 C6 6.79E-04 C20 1.16E-01 C21 -3.49E-02 C22 -4.36E-03 C23
-1.56E-03 C24 2.03E-03 C40 5.09E-03 C41 5.04E-04 C42 -9.55E-05 C60
-9.17E-04 S2 C2 8.57E-02 C3 2.21E-03 C4 -5.59E-03 C5 1.11E-03 C6
6.39E-04 C20 1.50E-01 C21 5.01E-02 C22 -4.53E-04 C23 -6.01E-04 C24
1.36E-03 C40 1.80E-02 C41 6.80E-03 C42 4.70E-04 C60 -2.69E-03 S3 C2
2.65E-02 C3 8.82E-03 C4 5.52E-03 C5 -7.09E-04 C6 -1.80E-04 C20
8.42E-02 C21 2.81E-02 C22 1.70E-02 C23 1.80E-03 C24 -2.28E-03 C40
1.84E-02 C41 -9.73E-04 C42 -2.91E-03 C60 -2.54E-03 S4 C2 6.02E-02
C3 -2.71E-02 C4 1.14E-02 C5 -3.05E-03 C6 1.16E-04 C20 1.46E-01 C21
-9.51E-02 C22 3.53E-02 C23 -7.42E-03 C24 -7.56E-04 C40 1.84E-02 C41
-1.03E-02 C42 -1.95E-03 C60 -1.36E-03 S10 C2 -1.16E-03 C3 2.41E-02
C4 7.57E-03 C5 1.40E-04 C6 -2.42E-03 C20 6.13E-02 C21 -1.73E-02 C22
-9.72E-04 C23 -3.76E-03 C24 -1.24E-02 C40 2.09E-02 C41 2.17E-03 C42
-1.24E-02 C60 -7.28E-03 S11 C2 -3.66E-02 C3 7.74E-02 C4 1.09E-02 C5
1.78E-03 C6 -1.91E-03 C20 -4.09E-02 C21 1.24E-01 C22 1.66E-02 C23
-7.87E-04 C24 -1.11E-02 C40 8.04E-03 C41 6.33E-03 C42 -2.80E-03 C60
-1.36E-03 S12 C2 -7.34E-03 C3 2.08E-02 C4 -1.03E-02 C5 -2.79E-03 C6
1.45E-04 C20 -6.60E-02 C21 8.10E-02 C22 1.89E-02 C23 -8.15E-04 C24
-1.28E-03 C40 -8.07E-03 C41 -1.81E-02 C42 -5.14E-03 C60 -3.59E-03
S13 C2 -3.20E-02 C3 -2.87E-02 C4 -1.03E-02 C5 -3.43E-03 C6 3.99E-04
C20 -7.99E-02 C21 -9.48E-02 C22 3.32E-02 C23 -4.09E-04 C24 3.92E-04
C40 -1.53E-02 C41 -2.33E-02 C42 3.53E-03 C60 -4.54E-04 S14 C2
-2.18E-01 C3 4.56E-03 C4 -2.58E-02 C5 -3.07E-03 C6 1.22E-02 C20
-2.29E-01 C21 -5.18E-02 C22 8.42E-02 C23 2.59E-02 C24 8.84E-04 C40
-3.23E-02 C41 1.53E-02 C42 -5.35E-03 C60 1.33E-02 S15 C2 -1.67E-01
C3 1.49E-02 C4 -2.87E-02 C5 -8.32E-03 C6 1.43E-02 C20 -6.27E-02 C21
-1.68E-03 C22 7.45E-02 C23 9.49E-03 C24 3.21E-03 C40 -2.11E-02 C41
3.64E-03 C42 -1.41E-02 C60 1.11E-02 S16 C2 1.80E-01 C3 1.02E-03 C4
-5.50E-03 C5 3.65E-05 C6 -9.26E-03 C20 2.19E-01 C21 -1.40E-02 C22
3.77E-02 C23 6.55E-03 C24 -6.45E-03 C40 3.38E-02 C41 -1.26E-03 C42
-7.92E-03 C60 -4.67E-03 S17 C2 1.99E-01 C3 -8.04E-03 C4 1.96E-02 C5
6.80E-03 C6 -2.56E-02 C20 1.21E-01 C21 -2.10E-02 C22 4.81E-02 C23
8.57E-03 C24 -1.03E-02 C40 8.75E-02 C41 -3.80E-04 C42 -1.02E-02 C60
-1.60E-02
TABLE-US-00025 TABLE 25 e e' e/e' 1 4.74959 4.29297 1.106365 2
4.83084 4.32908 1.115905 3 5.01599 4.34547 1.154303 4 5.71758 4.338
1.318022 5 2.75974 4.33504 0.636612 6 4.0421 4.38994 0.920764
TABLE-US-00026 TABLE 26 Surface Refractive Abbe Object surface Type
of surface interval index number Reference Flat surface 0 plane s0
s1 XY polynomial surface 0.6 1.48749 70.4 s2 XY polynomial surface
0.2 s3 XY polynomial surface 0.6 1.48749 70.4 s4 XY polynomial
surface 0.6 Diaphragm Flat surface 1.6 surface s5 s6 XY polynomial
surface 0.5 1.5219 67 s7 XY polynomial surface 0.1 s8 XY polynomial
surface 0.5 1.615232 51.2 s9 XY polynomial surface 0.9 s10 XY
polynomial surface 0.5 1.48749 70.4 s11 XY polynomial surface
3.0466 Image plane Flat surface
TABLE-US-00027 TABLE 27 Amount of deviation Telephoto Wide-angle
Lens number end Middle end E1 1.20411 1.03695 0.69269 E2 -1.19577
-0.82654 -0.12914 E3 -0.96144 -0.34862 0.7032 E4 -0.43232 -0.28899
-0.47989 E5 1.03109 0.40512 -0.28936
TABLE-US-00028 TABLE 28 s1 C2 -2.90E-02 C3 -4.82E-02 C4 -5.36E-03
C5 9.16E-04 C6 3.08E-04 C20 9.01E-02 C21 -8.09E-02 C22 -9.40E-04
C23 1.18E-02 C24 3.99E-03 C40 -6.81E-03 C41 1.06E-02 C42 7.80E-03
C60 1.88E-03 s2 C1 -1.00E-01 C2 -4.88E-02 C3 -2.09E-02 C4 -3.09E-03
C5 1.35E-03 C6 2.94E-04 C20 5.63E-02 C21 -3.53E-02 C22 8.12E-03 C23
1.82E-02 C24 4.66E-03 C40 -2.02E-02 C41 2.09E-02 C42 1.06E-02 C60
1.03E-02 s3 C1 -2.22E-02 C2 5.87E-03 C3 4.20E-02 C4 -5.51E-03 C5
-4.97E-04 C6 3.47E-04 C20 -2.68E-02 C21 1.41E-01 C22 1.41E-02 C23
-1.93E-02 C24 6.55E-03 C40 1.48E-03 C41 -3.87E-02 C42 1.83E-02 C60
4.02E-03 s4 C2 2.06E-02 C3 1.42E-02 C4 -4.73E-03 C5 -2.94E-03 C6
7.68E-04 C20 -4.00E-02 C21 9.09E-02 C22 3.21E-02 C23 -2.29E-02 C24
3.82E-03 C40 2.80E-02 C41 -5.20E-02 C42 1.86E-02 C60 -6.72E-03 s5
C2 -6.00E-02 C3 -6.72E-02 C4 -5.53E-03 C5 8.74E-03 C6 1.06E-03 C20
-1.21E-02 C21 7.62E-02 C22 1.81E-02 C23 -2.88E-02 C24 -8.36E-03 C40
9.74E-03 C41 -2.50E-02 C42 -1.82E-02 C60 8.84E-03 s7 C1 -9.23E-04
C2 -1.25E-02 C3 -1.16E-02 C4 4.78E-03 C5 9.30E-03 C6 1.11E-04 C20
2.66E-02 C21 1.55E-01 C22 3.01E-02 C23 -1.29E-02 C24 -4.03E-03 C40
-1.43E-01 C41 -2.42E-03 C42 -1.01E-02 C60 6.56E-02 s8 C1 5.94E-02
C2 -2.95E-02 C3 1.79E-02 C4 3.27E-03 C5 5.06E-03 C6 -2.95E-03 C20
4.76E-02 C21 1.50E-01 C22 2.89E-03 C23 -2.59E-02 C24 6.41E-03 C40
-1.41E-01 C41 5.46E-03 C42 -1.64E-02 C60 2.85E-02 s9 C1 1.27E-01 C2
-1.22E-01 C3 -2.06E-02 C4 9.78E-03 C5 3.74E-03 C6 -3.52E-03 C20
-7.64E-02 C21 1.27E-01 C22 -6.38E-03 C23 -2.48E-02 C24 7.39E-04 C40
2.57E-05 C41 -9.17E-03 C42 -2.01E-02 C60 -1.28E-03 s10 C1 -2.89E-02
C2 -1.21E-01 C3 3.59E-02 C4 -2.18E-02 C5 -5.47E-03 C6 3.16E-03 C20
-2.69E-01 C21 1.38E-01 C22 -2.02E-02 C23 -1.76E-02 C24 -7.12E-03
C40 3.86E-02 C41 -2.21E-02 C42 -1.40E-02 C60 8.06E-03 s11 C2
3.66E-02 C3 3.51E-02 C4 -1.22E-02 C5 -3.40E-03 C6 2.64E-03 C20
-7.75E-02 C21 5.37E-02 C22 9.63E-03 C23 -5.73E-03 C24 -1.98E-03 C40
1.13E-02 C41 -9.72E-03 C42 -5.94E-03 C60 -3.64E-04
TABLE-US-00029 TABLE 29 Comparative example 2 Example 1 Example 2
Example 3 Example 4 Example 5 .phi. of E7 Telephoto end 0.070555
0.0524264 0.026859 0.0568105 -0.048357 -0.176985 Middle 0.070555
0.0451396 0.0244142 0.0568155 -0.044729 -0.160276 Wide-angle
0.070555 0.0441824 0.0250744 0.0568155 -0.043986 -0.159685
Differences 0 0.008244 0.0024448 5E-06 0.0043708 0.0173 Difference
.times. diagonal length 0 0.037098 0.0110016 2.25E-05 0.0196686
0.07785 .phi. of G1 Telephoto end 0.092751 0.092899 0.100731
0.0994485 0.0915985 0.202515 Middle 0.021375 0.0248308 0.0387807
0.0346099 0.0296608 0.151895 Wide-angle -0.18425 -0.16593 -0.158782
-0.16345 -0.175728 0.0666744 Differences 0.276998 0.258829 0.259513
0.2628985 0.2673265 0.1358406 Difference .times. diagonal length
1.246491 1.1647305 1.1678085 1.1830433 1.2029693 0.6112827 .phi. of
G3 Telephoto end -0.58115 -0.552922 -0.515653 -0.455917 -0.512315
-0.07615 Middle -0.10308 -0.099618 -0.086842 -0.053169 -0.049238
0.0498576 Wide-angle 0.197742 0.188682 0.216735 0.224316 0.277264
0.212012 Differences 0.778892 0.741604 0.732388 0.680233 0.789579
0.2881619 Difference .times. diagonal length 3.505014 3.337218
3.295746 3.0610485 3.5531055 1.2967286 |.phi. d|min/ |.phi. d| --
31.396046 106.14897 52579.7 61.161915 7.8520578
TABLE-US-00030 TABLE 30 Type of surface Curvature radius Surface
interval Refractive index Abbe number Object surface Infinity S1
Polynomial surface 0.5 1.48749 70.4 S2 Polynomial surface 0.3 S3
Polynomial surface 0.5 1.48749 70.4 S4 Polynomial surface 0.1 S5
Spherical surface 1.811351 0.5 1.48749 70.4 S6 Spherical surface
1.593065 0.837525 S7(diaphragm Flat surface 0.337252 surface) S8
Spherical surface 2.618194 0.5 1.48749 70.4 S9 Spherical surface
9.964944 0.825224 S10 Polynomial surface 0.6 1.48749 70.4 S11
Polynomial surface 0.5 S12 Polynomial surface 0.6 1.48749 70.4 S13
Polynomial surface Variable S14 Spherical surface 2.997087 0.7
1.563804 63.7 S15 Spherical surface 2.925063 Variable Image plane
Flat surface
TABLE-US-00031 TABLE 31 Amount of deviation Lens Telephoto number
end Middle Wide-angle end E1 0.8603 0.40646 -0.8496 E2 -0.8603
-0.40646 0.8496 E5 -1.42634 -0.47734 0.74018 E6 1.42635 0.47734
-0.74018
TABLE-US-00032 TABLE 32 Amount of movement Surface in optical-axis
direction interval Telephoto end Middle Wide-angle end S13 0.1161
1.60533 1.46085 S15 3.0839 1.59467 1.73915
TABLE-US-00033 TABLE 33 S2 C2 0.064011 C3 -0.03116 C4 -0.01175 C5
-0.00116 C6 0.000393 C20 0.075119 C21 -0.04918 C22 0.002403 C23
0.002028 C24 0.002764 C40 0.005307 C41 0.002913 C42 -0.00149 C60
-0.00124 S3 C2 7.73E-02 C3 -1.15E-02 C4 -1.31E-02 C5 -1.25E-03 C6
3.24E-04 C20 7.44E-02 C21 1.20E-02 C22 7.50E-03 C23 4.11E-03 C24
2.40E-03 C40 2.53E-02 C41 7.20E-03 C42 -1.87E-03 C80 -3.60E-03 S4
C2 -2.22E-04 C3 2.72E-02 C4 1.07E-03 C5 -1.16E-03 C6 3.30E-04 C20
1.15E-01 C21 2.09E-02 C22 2.34E-02 C23 -6.92E-03 C24 -2.12E-03 C40
1.88E-02 C41 4.24E-04 C42 -1.82E-03 C60 -2.35E-03 S5 C2 1.07E-02 C3
1.99E-03 C4 2.77E-03 C5 -2.07E-03 C6 4.49E-04 C20 1.66E-01 C21
-7.04E-02 C22 4.04E-02 C23 -1.87E-02 C24 -2.97E-04 C40 4.18E-03 C41
-9.75E-03 C42 5.91E-04 C60 -1.83E-04 S11 C2 -6.17E-04 C3 1.68E-02
C4 7.78E-03 C5 -1.69E-03 C6 -1.27E-03 C20 6.32E-02 C21 2.77E-02 C22
1.45E-02 C23 -1.51E-02 C24 -8.81E-03 C40 1.39E-02 C41 -2.23E-02 C42
-2.21E-02 C60 -4.24E-03 S12 C2 -3.47E-02 C3 5.86E-02 C4 1.11E-02 C5
-1.03E-03 C6 -9.77E-04 C20 -5.60E-02 C21 1.62E-01 C22 3.50E-02 C23
-1.26E-02 C24 -7.53E-03 C40 1.04E-02 C41 -2.22E-02 C42 -1.79E-02
C60 -1.83E-03 S13 C2 3.67E-02 C3 4.05E-02 C4 -1.63E-02 C5 -3.14E-03
C6 6.66E-04 C20 -7.27E-02 C21 6.55E-02 C22 -1.64E-02 C23 -6.86E-03
C24 2.62E-03 C40 -4.94E-03 C41 9.24E-04 C42 -6.16E-05 C60 -4.63E-03
S14 C2 3.53E-03 C3 5.92E-03 C4 -1.10E-02 C5 -4.34E-03 C6 4.31E-04
C20 -4.00E-02 C21 -5.69E-02 C22 -5.75E-04 C23 -8.40E-03 C24
1.83E-03 C40 8.15E-03 C41 -3.22E-03 C42 1.40E-03 C60 -2.10E-03
TABLE-US-00034 TABLE 34 e e' e/e' 1 4.64019 4.45874 1.040695 2
4.68524 4.47408 1.047196 3 4.84857 4.49115 1.079583 4 5.38721
4.45972 1.20797 5 3.2979 4.56394 0.722599 6 4.32296 4.55333
0.949406
TABLE-US-00035 TABLE 35 Magnifying power E1 E2 E5 E6 E7 Telephoto
end 0 0.466035 1.507369 2.039752 0.879476 Middle 0 0.437331
1.117957 1.117665 0.896435 Wide-angle end 0 0.381325 0.00571
0.574456 0.89421
TABLE-US-00036 TABLE 36 Type of surface Curvature radius Surface
interval Refractive index Abbe number Object surface Infinity S1
Polynomial surface 0.5 1.563839 60.7 S2 Polynomial surface 0.1 S3
Polynomial surface 0.5 1.697002 48.5 S4 Polynomial surface 0.1
S5(diaphragm surface) Flat surface 0 S6 Polynomial surface 0.5
1.743198 49.3 S7 Polynomial surface 0.3 S8 Polynomial surface 0.5
1.697002 48.5 S9 Polynomial surface Variable S10 Aspheric surface
0.5 1.48749 70.2 S11 Aspheric surface -3 1.62536 S12 Aspheric
surface -1.38429 0.5 1.48749 70.2 S13 Aspheric surface -20.5692
Variable S14 Flat surface 2.970165 1.494 75 S15 Flat surface
1.51633 64.1 S16 Flat surface Image plane Flat surface
TABLE-US-00037 TABLE 37 Amount of deviation Lens number Telephoto
end Middle Wide-angle end E1 0.89063 0.0945 -0.20408 E2 -0.89063
-0.0945 0.20408 E3 -1.14918 -0.22964 0.09379 E4 1.14918 0.22964
-0.09379
TABLE-US-00038 TABLE 38 Amount of movement in optical-axis
direction Surface interval Telephoto end Middle Wide-angle end S9
2.77832 2.85902 2.83894 S13 0.496332 0.415639 0.43571
TABLE-US-00039 TABLE 39 A B S10 -0.00775 -0.02033 S11 0.042386
0.00162 S12 0.01989 -0.00842 S13 -0.00943 -0.00301
TABLE-US-00040 TABLE 40 A B S10 -0.00775 -0.02033 S11 0.042386
0.00162 S12 0.01989 -0.00842 S13 -0.00943 -0.00301
TABLE-US-00041 TABLE 41 S1 C2 0.049804 C3 -0.01866 C4 -0.00222 C5
-0.00043 C6 -3.8E-05 C20 0.039089 C21 -0.10081 C22 0.009658 C23
0.015455 C24 0.004319 C40 -0.01888 C41 0.00384 C42 0.007769 C60
0.010441 S2 C2 -1.04E-03 C3 3.35E-03 C4 1.34E-03 C5 1.06E-03 C6
2.40E-04 C20 -2.75E-02 C21 -6.05E-02 C22 3.06E-02 C23 3.32E-02 C24
5.75E-03 C40 6.26E-04 C41 1.09E-02 C42 8.73E-03 C60 3.84E-02 S3 C2
4.72E-02 C3 4.13E-02 C4 -8.18E-03 C5 6.82E-04 C6 1.94E-04 C20
-2.05E-02 C21 1.16E-01 C22 -2.36E-02 C23 -2.41E-03 C24 1.29E-02 C40
3.49E-02 C41 -4.08E-02 C42 1.85E-02 C60 5.50E-03 S4 C2 3.57E-03 C3
1.52E-02 C4 4.27E-04 C5 -1.37E-03 C6 2.17E-04 C20 -3.19E-02 C21
3.86E-02 C22 9.80E-03 C23 -8.82E-03 C24 6.36E-03 C40 2.86E-02 C41
-1.41E-01 C42 3.92E-02 C60 -3.15E-02 S6 C2 1.77E-02 C3 8.83E-03 C4
7.32E-03 C5 5.07E-04 C6 -6.67E-04 C20 3.76E-02 C21 2.14E-02 C22
2.27E-02 C23 1.57E-02 C24 -1.90E-02 C40 -3.08E-02 C41 -6.30E-02 C42
1.02E-03 C60 -1.31E-02 S7 C2 9.50E-03 C3 4.16E-02 C4 2.00E-03 C5
1.66E-03 C6 -4.20E-04 C20 -2.57E-02 C21 1.11E-01 C22 1.08E-02 C23
1.54E-02 C24 -1.43E-02 C40 -8.12E-02 C41 1.96E-02 C42 -1.07E-02 C60
3.53E-02 S8 C2 3.94E-03 C3 2.01E-02 C4 6.19E-03 C5 4.43E-04 C6
-2.59E-04 C20 -1.91E-02 C21 1.32E-03 C22 5.29E-02 C23 3.14E-02 C24
-1.75E-03 C40 -4.54E-02 C41 1.25E-03 C42 -4.47E-03 C60 3.60E-02 S9
C2 -2.81E-03 C3 -4.45E-03 C4 4.62E-03 C5 5.88E-04 C6 5.69E-05 C20
1.87E-02 C21 -4.74E-02 C22 3.77E-02 C23 2.52E-02 C24 1.58E-03 C40
-5.16E-03 C41 3.37E-04 C42 -2.97E-03 C60 8.63E-03
TABLE-US-00042 TABLE 42 Magnifying power E1 E2 E3 E4 E5 E6 Tele- 0
0.486578 1.445043 1.764707 0.424062 1.261455 photo end Middle 0
0.481248 1.120378 1.104816 0.424243 1.261209 Wide- 0 -0.80056
-0.13916 0.575994 0.42375 1.261915 angle end
Also, embodiments and modifications of at least one exemplary
embodiment include the following.
A zoom optical system in which multiple optical groups of which
optical power is variable and one or more optical groups are
disposed in the optical-axis direction for performing zooming by
changing the power of the multiple optical groups of which optical
power is variable, where the multiple optical groups of which
optical power is variable have multiple optical elements Ld each
including a rotationally asymmetrical surface for moving in the
direction in the direction different from the optical axis to
change the power within the optical group, and the one or more
optical groups include an optical group S having one or more
optical elements Ls which have symmetry as to at least one surface
and can perform decentering.
A zoom optical system in which multiple optical groups of which
optical power is variable and two or more optical groups are
disposed in the optical-axis direction for performing zooming by
changing the power of the multiple optical groups of which optical
power is variable, where the multiple optical groups of which
optical power is variable have multiple optical elements Ld each
including a rotationally asymmetrical surface for moving in the
direction in the direction different from the optical axis to
change the power within the optical group, and where the two or
more optical groups include an optical group S having one or more
optical elements Ls which have symmetry as to at least one surface
and can perform decentering, and an optical group C of which
optical power is substantially unchangeable.
The one or more optical elements Ls can be capable of decentering
include an optical element Lss for shifting in the direction
different from the optical axis.
The one or more optical elements Ls can be capable of decentering
include an optical element Lst for tilting.
EMBODIMENT 5
The sign of the optical power of the optical group C can be
unchangeable within the entire zoom range.
When the maximum value of the absolute value of the optical power
in the multiple optical groups of which optical power is variable
is |.PHI.d|max at the entire zoom positions, the maximum value of
the absolute value of the optical power in the optical group S is
|.PHI.s|max at the entire zoom positions, the following condition
|.PHI.s|max<|.PHI.d|max can be satisfied.
The one or more optical elements Ls can be capable of decentering
include an optical element Lss for shifting in the direction
different from the optical axis, the multiple optical elements Ld
include an optical element Lds for shifting in the direction
different from the optical axis, and when assuming that the maximum
value of the absolute value of the amount of shift of the optical
element Lds is |Dd|max at the entire zoom positions, and the
maximum value of the absolute value of the amount of shift of the
optical element Lss is |Ds|max at the entire zoom positions, the
following condition |Ds|max<|Dd|max can be satisfied.
When moving in the direction different from the optical axis, the
principal-point position of an optical group including the multiple
optical elements Ld is the optical-axis direction, the multiple
optical elements Ld include an optical element, which can have a
shape for moving outside of the optical group.
When assuming that the forward principal-point position and
backward principal-point position of an optical group A of the
multiple optical groups of which optical power is variable are
H.sub.A and H.sub.A' respectively, the forward principal-point
position and backward principal-point position of an optical group
B closer to the image side than the optical group A are H.sub.B and
H.sub.B', the distance between the object point and the forward
principal-point position H.sub.A is eo, the distance between the
backward principal-point position H.sub.A' and forward
principal-point position H.sub.B is e, the distance between the
backward principal-point position H.sub.B' and the image point is
ei, and a smaller distance between the distance eo and distance ei
is e', the distance e and distance e' are essentially the same at
an arbitrary zoom position.
Here, the following condition 0.7<e/e'<1.4 can be
satisfied.
When assuming that of the multiple optical groups of which optical
power is variable, the backward principal-point position of the
optical group A is H.sub.A', the forward principal-point position
of the optical group B closer to the image side than the optical
group A is H.sub.B, the distance between the backward
principal-point position H.sub.A' and forward principal-point
position H.sub.B in a case in which the power of the entire system
is the minimum within the range of the positive optical power of
the area where the optical power of the optical group A is variable
is et1, the distance between the backward principal-point position
H.sub.A' and forward principal-point position H.sub.B in a case in
which the power of the entire system is the maximum within the
range of the positive optical power of the area where the optical
power of the optical group A is variable is ew1, the distance
between the backward principal-point position H.sub.A' and forward
principal-point position H.sub.B in a case in which the power of
the entire system is the minimum within the range of the negative
optical power of the area where the optical power of the optical
group A is variable is et2, and the distance between the backward
principal-point position H.sub.A' and forward principal-point
position H.sub.B in a case in which the power of the entire system
is the maximum within the range of the negative optical power of
the area where the optical power of the optical group A is variable
is ew2, the following conditions et1<ew1 et2<ew2 can be
satisfied.
When assuming that an optical group of the multiple optical groups
of which optical power is variable is an optical group A, and an
optical group closer to the image side than the optical group A is
an optical group B, the maximum value of the absolute value of the
optical power between the optical groups A and B in the entire zoom
range is |.PHI.|max. Furthermore, a first variable optical power
.PHI.1, a second variable optical power .PHI.2, and the value of
sum of the optical power in an arbitrary zoom position of the first
and second variable optical power units can be expressed as
.PHI.AB=.PHI.1+.PHI.2, where the following condition
-|.PHI.|max.ltoreq..ltoreq..PHI.AB.ltoreq..ltoreq.|.PHI.|max can be
satisfied.
The zoom optical system can include an optical group of which
optical power is variable, a lens group (lens unit) of which
optical power is substantially unchangeable, an optical group of
which optical power is variable, and an optical group having an
optical element capable of decentering, in order from the object
side toward the image side.
The one or more optical elements Ls can be capable of decentering
perform decentering so as to correct and/or reduce the residual
aberration of the optical group of which optical power is variable
or/and an aberration to be generated when attempting to change
optical power.
A zoom optical system in which multiple optical groups of which
optical power is variable and one or more optical groups are
disposed in the optical-axis direction for performing zooming by
changing the power of the multiple optical groups of which optical
power is variable, where the multiple optical groups of which
optical power is variable have multiple optical elements Ld each
including a rotationally asymmetrical surface for moving in the
direction in the direction different from the optical axis to
change the power within the optical group, and the one or more
optical groups include an optical group S having one or more
optical elements Ls which have symmetry as to at least one surface
and can move in the optical-axis direction.
A zoom optical system in which multiple optical groups of which
optical power is variable and one or more optical groups are
disposed in the optical-axis direction for performing zooming by
changing the power of the multiple optical groups of which optical
power is variable, where the multiple optical groups of which
optical power is variable have multiple optical elements Ld each
including a rotationally asymmetrical surface for moving in the
direction different from the optical axis to change the power
within the optical group, and the one or more optical groups
include an optical group S having one or more optical elements Ls
which have symmetry as to at least one surface and can move in the
optical-axis direction, and an optical group C of which optical
power is substantially unchangeable.
The optical elements Ls can move at the time of zooming.
The one or more optical elements, which can move in the
optical-axis direction, can include an optical element having
positive refracting power.
When assuming the amount of movement in the entire zoom range of
one optical element of the one or more optical elements which can
move in the optical-axis direction is d, and the entire length of
the entire system is T, the following condition d/T<0.6 can be
satisfied.
When moving in the direction different from the optical axis, the
principal-point position of an optical group including the multiple
optical elements Ld is the optical-axis direction, and the multiple
optical elements Ld include an optical element, which can have a
shape for moving outside of the optical group.
When assuming that the forward principal-point position and
backward principal-point position of an optical group A of the
multiple optical groups of which optical power is variable are
H.sub.A and H.sub.A' respectively, the forward principal-point
position and backward principal-point position of an optical group
B closer to the image side than the optical group A are H.sub.B and
H.sub.B', the distance between the object point and the forward
principal-point position H.sub.A is eo, the distance between the
backward principal-point position H.sub.A' and forward
principal-point position H.sub.B is e, the distance between the
backward principal-point position H.sub.B' and the image point is
ei, and a smaller distance between the distance eo and distance ei
is e', the distance e and distance e' are essentially the same at
an arbitrary zoom position.
Here, the following condition 0.7<e/e'<1.4 can be
satisfied.
When assuming that of the multiple optical groups of which optical
power is variable, the backward principal-point position of the
optical group A is H.sub.A', the forward principal-point position
of the optical group B closer to the image side than the optical
group A is H.sub.B, the distance between the backward
principal-point position H.sub.A' and forward principal-point
position H.sub.B in a case in which the power of the entire system
is the minimum within the range of the positive optical power of
the area where the optical power of the optical group A is variable
is et1, the distance between the backward principal-point position
H.sub.A' and forward principal-point position H.sub.B in a case in
which the power of the entire system is the maximum within the
range of the positive optical power of the area where the optical
power of the optical group A is variable is ew1, the distance
between the backward principal-point position H.sub.A' and forward
principal-point position H.sub.B in a case in which the power of
the entire system is the minimum within the range of the negative
optical power of the area where the optical power of the optical
group A is variable is et2, and the distance between the backward
principal-point position H.sub.A' and forward principal-point
position H.sub.B in a case in which the power of the entire system
is the maximum within the range of the negative optical power of
the area where the optical power of the optical group A is variable
is ew2, the following conditions et1<ew1 et2<ew2 can be
satisfied.
When assuming that an optical group of the multiple optical groups
of which optical power is variable is an optical group A, and an
optical group closer to the image side than the optical group A is
an optical group B, in the event of zooming from the telephoto end
toward the wide-angle end, the power of the optical group A changes
from positive to negative, the power of the optical group B changes
from negative to positive, a zoom position where the optical power
of the optical group A matches with the optical power of the
optical group B exists in the entire zoom range, and the matched
zoom position is closer to the wide-angle side than the middle zoom
position within the entire zoom range.
When assuming that of an optical group A and an optical group B
closer to the image side than the optical group A of the multiple
optical groups of which optical power is variable, a greater one of
which the absolute value of the optical power at the wide-angle end
is |.PHI.gw|max, and a smaller one of which the absolute value of
the optical power at the telephoto end is |.PHI.gt|min, the
following condition |.PHI.gw|max<|.PHI.gt|min can be
satisfied.
When assuming that an optical group of the multiple optical groups
of which optical power is variable is an optical group A, and an
optical group closer to the image side than the optical group A is
an optical group B, the maximum value of the absolute value of the
optical power between the optical groups A and B in the entire zoom
range is |.PHI.|max, and the total value of the optical power of
the optical group A and optical group B at an arbitrary zoom
position is .PHI..sub.AB, the following condition
-|.PHI.|max.ltoreq..PHI.AB.ltoreq.|.PHI.|max can be satisfied.
When assuming that of the entire zooming range, the maximum value
of the values obtained by dividing the maximum value of the
absolute value of the image-forming magnification of each of the
multiple optical elements Ld by the minimum value is Bd max, and
the minimum value of the values obtained by dividing the maximum
value of the absolute value of the image-forming magnification of
each of the one or more optical elements Ls by the minimum value is
Bs min, the following condition Bs min<Bd max can be
satisfied.
When assuming that the amount of change in the optical-axis
direction caused by zooming from the telephoto end toward the
wide-angle end of the forward principal-point position H.sub.A of
the optical group A of the multiple optical groups of which optical
power is variable is .DELTA.H.sub.A, the amount of change in the
optical-axis direction caused by zooming from the telephoto end
toward the wide-angle end of the forward principal-point position
H.sub.B of the optical group B closer to the image side than the
optical group A is .DELTA.H.sub.B, greater amount of change between
the amount of change .DELTA.H.sub.A and the amount of change
.DELTA.H.sub.B is .DELTA.H.sub.d max, and the amount of change of
the forward principal-point position of the one or more optical
elements Ls is .DELTA.H.sub.S, the following condition
.DELTA.H.sub.S<.DELTA.H.sub.d max can be satisfied.
An image can be formed on a photoelectric conversion element.
An imaging apparatus can including the zoom optical system, and a
photoelectric conversion element for photo-accepting an image
formed by the zoom optical system.
While the present invention has been described with reference to
exemplary embodiments, it is to be understood that the invention is
not limited to the disclosed exemplary embodiments. The scope of
the following claims is to be accorded the broadest interpretation
so as to encompass all modifications, equivalent structures and
functions.
This application claims the benefit of Japanese Applications No.
2005-186984 filed Jun. 27, 2005, and No. 2005-186961 filed Jun. 27,
2005, which are hereby incorporated by reference herein in their
entirety.
* * * * *